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====== Wet & Wild study group, common blog ======

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<span style="color:red;font-size:80%;text-align:right;">please check this page a few times a week, there will be no emails</span>
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John G: I was wondering if you could put up an example script that you would qsub to the cluster.  I got channelflow to compile on in my home directory on pacemaker, and all that is left for me to do is exploit the raw computing power. There is also a small error (that I've found) in the continuesoln code that needs to be adjusted.  continuesoln, for equilibria, generates T.asc files.  If you want to read in solutions that already exist, however, continuesoln wants to read in Tbest.asc.  In the next distribution, that would be worth correcting. ---//[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-06-17 12:00// 

{{gtspring2009:gibson.png?24 }} I'll be off in Minnesota for two weeks, June 13th-27th ([[http://www.cns.gatech.edu/~gibson/travel.txt|schedule, phone numbers]]). Just wanted to alert you all. Internets access will be spotty but I will check in when I can.

{{gtspring2009:pc.jpg}} Notes on [[gtspring2009:gibson:eq8|Itano and Generalis paper]]. Nothing earthshaking - there are a few unanswered questions among the comments marked red. Their visualization is very pretty. It is interesting how hard (or impossible) is to recognize the same equilibrium from different visualizations.

{{gtspring2009:gibson.png?24 }} The P47.18 orbit and others in the W03/GHC cell are now posted on the [[database]]. 
Continuation of solutions via repeated changegrid and findorbit should work fine. When you get the hang of that, try out the continuation utility. Its advantages  are speed (it can take larger steps in parameter space), automation, and ability to continue around a corner from a lower to and upper branch (or vice versa). /// John Gibson 2009-06-05 12:22 EST//

Hey John, could you post a data file for the 47.18 periodic orbit for me.  Thanks.  Also, I have generated about 90 flow fields that I think are continuations of the Upper Branch Solution.  I say "I think" because instead of using the continue solution utility, I used changegrid then I used findorbit to find a solution.  Do these calculations have merit or do I need to use continuesoln? --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-06-02 09:24//

{{gtspring2009:gibson.png?24 }} Hi, Dustin. Sorry for the wait. I was at a conference, then had a long weekend, and now computer trouble (am reinstalling SUSE-11.1 on my home desktop as we speak). It sounds to me like findorbit is looking for equilibrium solutions rather than periodic orbits. The current version requires you to specify -orb or -eqb, which adds/removes the integration time T to/from the search space. If the version you're running doesn't require -orb or -eqb, it defaults to one or the other. Run findorbit -h to see which. I bet it defaults to eqb, in which case T=47 is a long time and close enough to the period of the unstable oscillation around EQ2 that it might be stuck in a local minimum. //John Gibson 2009-05-27 11:33 EST//

//For John G//: John, I had a quick question about the convergence of the findorbit program and you haven't been on Skype recently to talk about it.  Recently I was seeing if the 47.18 Periodic orbit could be found from flow fields represented on the poincare sections I was producing.  Close to the solution along the unstable manifold, findorbit only found the Upper Branch Equilibrium, even though I specified that the solution it should be looking for was periodic.  But that is of secondary concern right now.  I moved a little farther away from the equilibrium solution, and ran findorbit with the same input, namely:

    findorbit -T 47.18 uPo4.ff

The run went through all 20 Newton hook steps and converged to a r(u,t) of about 0.0006.  Because this was working well (at least I think), I saved all the data I had generated into a directory and continued the calculation using ubest.ff.  Now the r(u,t) value, after another 18 Newton Hook Steps has only decreased to about 0.0003.  Do you think that this calculation is still worth pursuing.  I could send you the log files if you think your perusal would shed some light on the situation. --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-05-20 10:13//


{{gtspring2009:jshyatt.jpg?24}} Everybody:  I have been really sick with something I caught at the end of finals :-(  I'm better now and will be going back to work on 8-fold symmetry equilibria as per my orders from John G unless someone tells me otherwise.  I need to get a PACE account, which I think involves someone emailing the OIT guy?  //John Hyatt 2009-05-10 14:42//

{{gtspring2009:pc.jpg}} added [[:chaosbook:pcf|a link]] to the interesting [[http://arxiv.org/abs/0904.4676|Li and Lin paper]] on laminar stability  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-05-01 05:01//

{{gtspring2009:pc.jpg}} A [[gtspring2009:gibson:w03#desymmetrized_poincare_sections|desymmetrized plot of Poincare sections]]? Also, check out [[http://www.dynamicalsystems.org/ma/|Dynamical Systems Magazine]]: our tutorial is featured, with somewhat misleading abstract --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-04-27 08:02//

{{gtspring2009:siminos.png?24}} Join the the [[chaosbook:howto:proofreading#bibtex_conventions|spirited bibtex discussion]]  -- //[[dborrero@gatech.edu|Daniel Borrero]] 2009-04-16 14:28 EST//

{{gtspring2009:gibson.png?24}} [[gtspring2009:gibson:w03#poincare_sections_4|Disappointing Poincare section results]]. 
I will explain these plots tomorrow in the study group. Corrections and suggestions are welcome. // John Gibson 2009-04-13 14:58 EST//

{{gtspring2009:jshyatt.jpg?24}}  I'd like to talk to someone about me doing some actual research - more in the [[:gtspring2009:research_projects:hyatt:blog#nite_fishin|nite fishin']] blog.  //John Hyatt 2009-04-09 13:41//

{{gtspring2009:gibson.png?24}} [[gtspring2009:gibson:continuation#hkw_orbit_continuation|Continuation of HKW orbits in Re.]]
Ran 1,500th PACE job this weekend, since March 2008. If only that were publications.... // John Gibson 2009-04-06 12:27 EST//

{{gtspring2009:gibson.png?24}} Comments on [[gtspring2009:spieker_blog:ub_eigenvectors:color_scaling]] and
another argument to not plot eigenvectors superimposed on the laminar flow. //John Gibson 2009-04-03 14:22 EST//

{{gtspring2009:gibson.png?24}} John H: The problems with your blog were caused by a missing %%]%% to close off 
a link in my recent post --sorry. I found the error by looking in the dokuwiki source near the last word before the strange cut-off.  //John Gibson 2009-04-03 10am EST//

:-(  Having problems updating my blog...every time I try to edit or restore an old edit it goes back to what it is now, where some of John G's most recent post and all of my response to it have vanished.  I will try again tomorrow. //John Hyatt 2009-04-03 3:00//

{{gtspring2009:gibson.png?24}} 1. [[gtspring2009:spieker_blog:ub_eigenvectors:laminar|why not to **add** laminar to plots of eigenfunctions]]. 2. In case you haven't noticed, there is a "Recent changes" button at the top right of the each page. It's a good way to find recent edits. 3. [[gtspring2009:research_projects:hyatt:blog#nite_fishin|responses in hyatt nite fishin blog]]. 4. Boo-hoo, why doesn't any ever call? // John Gibson 2009-04-01 //
 

{{gtspring2009:pc.jpg}} Have I [[gtspring2009:spieker_blog:ub_eigenvectors:first_try|labeled UB eigenvectors correctly]]? (Re **e**_11,Im **e**_11) is the least contracting stable eigenvalue pair? Also, a  vote against [[gtspring2009:spieker_blog:ub_eigenvectors:laminar|subtracting laminar]] from eigenvectors. --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-31//

{{:gtspring2009:gt.png|}} Wiki-training of Professor Tanner on the tricky chapter [[:chaosbook:conjug|"Get straight"]]   --- //[[gregor.tanner@nottingham.ac.uk|Gregor Tanner]]  2009-3-26//

:-) Added twelve [[gtspring2009:spieker_blog#eigenvectors_of_the_ub_equilibrium|plots]] of the eigenvectors for the upper branch equilibrium to my blog. --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-27//

{{gtspring2009:paprocki1.jpg?24}} Finally added a more complete description of the [[gtspring2009:2dturbulence
|2D turbulence experiment]] .  Please let me know if I need to elaborate or am unclear on anything. //[[jon.paprocki@gatech.edu|Jon Paprocki]] 2009-03-26 2:20 PM//

{{gtspring2009:paprocki1.jpg?24}} New recurrence plots showing some interesting behavior between periodic and turbulent flow at [[gtspring2009:2dturbulence]]  EDIT: added corresponding movies of the runs and velocity fields //[[jon.paprocki@gatech.edu|Jon Paprocki]] 2009-03-26 1:04 PM//

{{gtspring2009:gibson.png?24}} Note on [[gtspring2009:howto:format#how_to_resize_pngs | how to note on resize PNGs]]. //John Gibson 2009-03-25 13:54 EST//

{{gtspring2009:pc.jpg}} to all channelflow groupies: can you plot the first few W03 upper branch eigenvectors in the [[gtspring2009:howto:format#preferences|standard *.png 400x300 pixels format]]? Needed for [[http://chaosbook.org/tutorials/index.html|DasTutorial]].

{{gtspring2009:pc.jpg}} Re [[gtspring2009:howto:format|howto:format]] page: I would like to get the [[http://apps3.aps.org/gsnp/galleryinfo.cfm|APS Nonlinear Gallery]] to require flash and flash only (at least half of the formats used this year needed downloading things like [[http://www.videolan.org/vlc/|VLC media player]] in order to be seen).

{{gtspring2009:gibson.png?24}} Study group participants: Don't be shy about calling me. johnfgibson on skype, 617-441-3609 on phone. I have a brand-new, clear-as-a-bell headset for skype. //John Gibson 2009-03-25 10:53 EST// 
\\
{{gtspring2009:pc.jpg}} Same here - if I'm on skype, call - I can help with dynamical systems kinds of questions.  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-25 07:58//

{{gtspring2009:gibson.png?24}} [[gtspring2009:gibson:w03#more_poincare_sections| New Poincare sections]].
It's hard to interpret 2D slices of 10^5 dimensions. Comments appreciated. //John Gibson 2009-03-24 14:56 EST//


{{gtspring2009:gibson.png?24}} New channelflow tarball on [[download]] page. Should help in compilation of
poincare section code. //John Gibson 2009-24-09 12:16 EST//

:-\ The [[:gtspring2009:research_projects:hyatt:blog#nite_fishin|nite fishin']] project started  --- //[[jshyatt@gatech.edu|John Hyatt]] 2009-03-20//

{{gtspring2009:gibson.png?24}} Wrote [[gtspring2009:howto:poincare | How to compute a Poincare section]]. Not for the faint of heart.
Also, [[gtspring2009:gibson:w03#and_more|more on factoring out the 4th-order translation symmetry]]. //John Gibson 2009-03-20 12:29 EST//

{{gtspring2009:gibson.png?24}} [[:chaosbook:discrete#quotienting_the_discrete_translation_pcf_symmetry|On quotienting the discrete translation pCf isotropy subgroup]]  --- // John F. Gibson 2009-03-19//

{{gtspring2009:gibson.png?24}} [[gtspring2009:gibson:w03#poincare_section|A Poincare section]] of the Nagata upper branch unstable manifold. Just a first stab. --- // John F. Gibson 2009-03-17//

{{gtspring2009:pc.jpg}} There are some nice movies in this year's APS gallery of nonlinear dynamics. In particular, JohnE and JohnG, check out [[http://apps3.aps.org/gsnp/upload/KlausRoeller.mov|Unstable Kolmogorov flow in granular matter]] - different physics, but strikingly like our plane Couette.  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-15 10:43//

{{gtspring2009:pc.jpg}} to JohnH: read [[gtspring2009:howto:movie#how_to_post_a_file|how_to_post_a_file]]?  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-12 21:08//

{{gtspring2009:gibson.png?24}}  Completed [[gtspring2009:gibson:continuation#section2|continuation of P19.02 orbit in Reynolds number]]. The plumbers are clamoring for this. Automation is unavoidable.
//John F. Gibson 2009-03-11 EST 15:42//

{{gtspring2009:gibson.png?24}}  
Please sign up for my [[gtspring2009:gibson:office_hours|office hours]] tomorrow if you would like to talk one-on-one about your project.
Proposal for tomorrow's meeting in the [[gtspring2009:schedule]] and comments on Dustin's
[[gtspring2009:howto:shell_scripts|shell scripting howto]]. // John Gibson 2009-03-09 12:27 EST//

:-) The [[gtspring2009:spieker_blog#projectpoincare_sections_and_return_maps|slice & dice]] project started  --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-06//

{{gtspring2009:pc.jpg }} added new material to  [[chaosbook:smale|Chapter: Qualitative dynamics, for cyclists]], mostly for Dustin or JohnG.  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-05 14:49//

{{gtspring2009:pc.jpg }} Pick [[gtspring2009:research_projects|your project]] by Tuesday, March 3 2009.

{{gtspring2009:pc.jpg }} made all clickable movies in 
[[http://chaosbook.org/tutorials/index.html|ChaosBook.org/tutorials]] flash. IExplorer woes: pop-ups come misformated, with all toolbars showing. If you have suggestions, please 
[[chaosbook:movies_of_plane_couette_-_tutorial#hiccups|blog them]]. Are flash pop-ups working for browsers you use?  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-27 03:11//

{{gtspring2009:gibson.png?24}} Posted new {{downloads:channelflow-1.3.4.tgz}} tarball with continuation and Poincare section
utilities. //John Gibson 2009-02-26 12:09 EST//

:-) Added a [[gtspring2009:howto|HowTo]] for writing script files.  Would like some feedback on that, so a user doesn't need to be so wary of doing what I said to do.  --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-26 06:02//

{{:gtspring2009:pc.png|}} [[gtspring2009:howto:blogging|A discussion of what to keep internal, what to open to google-eyed]]  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-22 16:07// 

{{:gtspring2009:pc.png|}} added links to videos, [[chaosbook:overheads|JF Gibson and P Cvitanovic Newton Institute 2008 presentations]]  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-22 16:07//

{{:gtspring2009:pc.png|}} added links to [[gtspring2009:howto:pace|PACE how-to]]  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-22 16:48//

{{gtspring2009:paprocki1.jpg?24}} Did a search for something between periodic and turbulent motion, results at [[gtspring2009:2dturbulence]].  EDIT: Added a couple comments.//[[jon.paprocki@gatech.edu|Jon Paprocki]] 2009-02-20 12:16 PM//

{{gtspring2009:siminos.png?24}} Continued discussion of problems with movies in [[gtspring2009:research_projects:siminos:blog|Siminos blog]]. --- //[[siminos@gatech.edu|Evangelos Siminos]] 2009-02-16 14:14//

{{gtspring2009:paprocki1.jpg?24}} Recurrence plots and accompanying movies of the runs and velocity fields for some "hybrid" runs combining periodic and turbulent motion posted to [[gtspring2009:2dturbulence]]. //[[jon.paprocki@gatech.edu|Jon Paprocki]] 2009-02-13 5:29 PM//

{{gtspring2009:gibson.png?24 }} Wrote quadratic continuation utility in which the cell size can vary. Continuation parameter is arbitrary. Enabled [[gtspring2009:gibson:continuation|continuation equilibria into previously uncharted territory]]. // John Gibson 2009-02-13 13:42 EST//

{{:gtspring2009:pc.png|}} added [[chaosbook:maps#poincare_sections|ChaosBook.org Chapter Discrete time dynamics]], exhorting the troops to slay the dragon by Poincaré sections.  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-11 13:49//

{{gtspring2009:gibson.png?24 }} A new periodic orbit P47.18 in the [[gtspring2009:gibson:w03|W03 cell]] that clings closely to the unstable manifold of the Nagata upper branch equilibrium. Predrag, you were right: there's a non-wandering set near the Nagata UB. Need to factor out 
the discrete symmetry and produce plots that show this orbit's relation to the UB unstable manifold more vividly. 

{{gtspring2009:gibson.png?24 }} Wrote documentation for construction of low-d basis and projection of trajectories in [[:docs:tutorial]]

{{gtspring2009:pc.jpg }} added [[gtspring2009:howto:format|howto format movies]] homepage  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-10 03:57//

{{gtspring2009:pc.jpg }} Vaggelis asks: [[gtspring2009:research_projects:siminos:blog|Why is decay to laminar so slow?]]  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-10 04:17//

{{gtspring2009:gibson.png?24 }} [[gtspring2009:gibson:blog#2009-02-08_movies_of_w03_orbits|Dual-view movies of new periodic orbits]].  //John Gibson 2009-02-08 22:19// P.S. Anyone care to join me with a micro-thumbnail headshot? Would require fewer brain cells than the smiley → person map.


{{gtspring2009:pc.jpg }}  [[gtspring2009:research_projects:shah:blog#chaos_and_gauge_field_theory|Sarang project]]  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-08 13:55//

{{gtspring2009:pc.jpg }}  starting to contemplate adding Gibsonite [[http://www.merriam-webster.com/cgi-bin/audio.pl?mellif02.wav=mellifluous%27|mellifluous]] voice track to [[chaosbook:movies_of_plane_couette_-_tutorial#adding_audio|DasTutorial]] (the other one)  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-08 13:55//

{{gtspring2009:gibson.png?24 }} [[gtspring2009:gibson:blog#w03_cell|Some new periodic orbits in the narrow cell]]. //John Gibson 2009-02-05 13:55// \\

{{gtspring2009:gibson.png?24 }} More on Roman's question on how Krylov subspace methods can find an answer to a singular Ax=b problem, 
when x = A<sup>-1</sup> b is  dominated by the huge eigenvalues of A<sup>-1</sup>. Krylov subspace methods 
work somewhat like SVD in finding a least-squares approximation to x. With SVD you project the original 
problem onto a subspace with no singular directions, and the solution to the projected problem is the 
least-squares solution to the original. I.e. you find the zero singular values and simply throw them away. 
The Krylov subspace methods are similar, in that they detect and learn to ignore singular directions 
because perturbations in those directions don't help reduce the least-squares residual |Ax-b|<sup>2</sup>. 
//John Gibson 2009-02-05 13:55// 

{{gtspring2009:pc.jpg }} several [[chaosbook:diffusion#rainer_klages|deterministic diffusion references]] added
 --- //[[r.klages@qmul.ac.uk|Rainer Klages]] 2009-02-03//

{{gtspring2009:gibson.png?24 }}  Magical movie incantations enumerated in new [[gtspring2009:howto:movie|movie-posting howto]]. Also, note the new [[gtspring2009:howto]] link at the top of this page,
for tips and tricks specific to our study group. // John Gibson 2009-02-04 15:42//

:-? posted LB unstable manifold videos on [[gtspring2009:research_projects:siminos:blog|Siminos blog]]. Need help
 --- //[[siminos@gatech.edu|Evangelos Siminos]] 2009-02-04 02:47//

:-) Dustin posted two videos of simulations he was eventually able to hack his way through. Links can be found on his [[gtspring2009:spieker_blog|blog]].  He is starting to get really excited about all of this. --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-03 16:25// That turns my 8-O into a ^_^! //John Gibson 2009-02-05 8:43//


:-D I have a question about the tutorial on the "hickups" [[gtspring2009:research_projects:hyatt:blog|blog]].  //[[jshyatt@gatech.edu|John Hyatt]] 2009-02-03 15:16//

:-P Posted links to Youtube videos of preliminary 2-D turbulence data to [[gtspring2009:2dturbulence|2-D Turbulence blog]].  -- //[[dborrero@gatech.edu|Daniel B.]] 2009-02-03 11:31//

{{gtspring2009:pc.jpg }}  G. Tanner commented on [[chaosbook:noise#gregor_tanner|noisy paper]] by Domenico and Predrag

{{gtspring2009:pc.jpg }}  created [[gtspring2009:blogofblogs|blogs]] for everyman
 --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-01 05:13//

:-? caught broken links in [[chaosbook:movies_of_plane_couette_-_tutorial|Movies of plane Couette - tutorial]]
 --- //[[siminos@gatech.edu|Evangelos Siminos]] 2009-02-03 02:47//

{{gtspring2009:gibson.png?24 }}  Posted [[movies:hkw|movies of periodic orbits of plane Couette flow]]; conversion of [[database]] to dokuwiki underway. //John G 2009-01-28 12:48//

{{gtspring2009:pc.jpg }}  answered [[gtspring2009:spieker_blog|Dustin blog]] question on how many stability eigenfunctions are needed
 --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-01-28 05:41//

{{gtspring2009:pc.jpg }}  added some [[chaosbook:graphics|notes on graphics software]]
 --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-01-28 05:10//

:-P [[gtspring2009:research_projects:borrero:blog|Daniel and John G]] on uploading images (to root:gtspring2009:research_projects:...) and movies - go flash! 
 --- //[[dborrero@gatech.edu|Daniel B.]] 2009-01-27 1:18//

{{gtspring2009:gibson.png?24 }}  For 2009-01-27 Tuesday's meeting  we will have a "channelflow installfest". For next week we'll have an assignment involving a calculation with channelflow. For more information, see the [[gtspring2009:schedule]].  --- //[[gibson@cns.physics.gatech.edu|John F. Gibson]], 2009-01-26 09:00//

{{gtspring2009:pc.jpg }}  added [[chaosbook:intro|ChaosBook.org Chapter Overture]] with general suggestions for betterment of DasBuch by Damon Lamb. Any such comments are very welcome.
 --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-01-16 09:33//

{{gtspring2009:pc.jpg }}  added [[chaosbook:noise|ChaosBook.org Chapter Noise]] where Domenico & Predrag go mano a mano with noisy heavyweights, discussing the paper just mentioned below.
 --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-01-14 08:34//

=) [[gtspring2009:research_projects:elton:blog|Lagrangian mixing notes]]: added slides and notes from 1/13 class
 --- //[[jelton.physics@gmail.com|John Elton]] 2009-01-13//
  *  //Predrag to John E.:// thanks, great to get the notes! Few tips:
    * feeblepoint presentations - too many words on this one
    * scanning - mail room downstairs has an amazing scanner, you run it by logging in with GTid, get a pdf out.

{{gtspring2009:pc.jpg }}  [[chaosbook:diffusion|ChaosBook.org blog]]: added discussion of why lack of structural stability is good news for chaos, and its experimental implications for plumbers. 
 --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-01-12 05:25//

{{gtspring2009:gibson.png?24 }}  [[:gtspring2009:research_projects:gibson:blog#state_space_portraits|Gibson blog - State-space portraits]]: added a set of HKW periodic orbit projections
 --- //[[gibson@cns.physics.gatech.edu|John F. Gibson]] 2009-01-07//
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