chaosbook:maps
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chaosbook:maps [2009/02/11 13:48] 127.0.0.1 external edit |
chaosbook:maps [2009/02/13 04:02] predrag |
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| (ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#maps|Discrete time dynamics]]) --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-11 12:55// | (ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#maps|Discrete time dynamics]]) --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-11 12:55// | ||
| - | ===== Poincaré sections ===== | + | ===== Section: Poincaré sections ===== |
| {{gtspring2009:pc.jpg }} If GaTech world domination is to be maintained, we need to start taking Poincaré sections of unstable manifolds. Make sure you understand chapters on [[http://chaosbook.org/paper.shtml#maps|Discrete time dynamics]], [[http://chaosbook.org/paper.shtml#stability|Local stability]] and [[http://chaosbook.org/paper.shtml#invariants|Cycle stability]]. --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-11 12:55// | {{gtspring2009:pc.jpg }} If GaTech world domination is to be maintained, we need to start taking Poincaré sections of unstable manifolds. Make sure you understand chapters on [[http://chaosbook.org/paper.shtml#maps|Discrete time dynamics]], [[http://chaosbook.org/paper.shtml#stability|Local stability]] and [[http://chaosbook.org/paper.shtml#invariants|Cycle stability]]. --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-11 12:55// | ||
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| {{gtspring2009:pc.jpg }} Constructing Poincaré sections and return (or forward) maps is not such a big deal - it's just that no masters of plumbing listen to my pleas. **Jul 6 2006** I got Halcrow to give it a try: | {{gtspring2009:pc.jpg }} Constructing Poincaré sections and return (or forward) maps is not such a big deal - it's just that no masters of plumbing listen to my pleas. **Jul 6 2006** I got Halcrow to give it a try: | ||
| - | {{:intro:returntimevsperturbation.png|}} | + | {{chaosbook:intro:returntimevsperturbation.png|}} |
| Poincaré return time to first intersection with a Poincaré section, normal to one of the eigenvectors corresponding to the most unstable complex pair of eigenvalues of the upper branch. | Poincaré return time to first intersection with a Poincaré section, normal to one of the eigenvectors corresponding to the most unstable complex pair of eigenvalues of the upper branch. | ||
| ~~CL~~ | ~~CL~~ | ||
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| With Y. Lan I had a bit more luck. He resisted for 6 years or so, but than his wife told him that thesis should be finished this semester and he relented. His Kuramoto-Sivashinsky ("fluid dynamics" in one dimension) plots all like the usual nonlinear garbage: | With Y. Lan I had a bit more luck. He resisted for 6 years or so, but than his wife told him that thesis should be finished this semester and he relented. His Kuramoto-Sivashinsky ("fluid dynamics" in one dimension) plots all like the usual nonlinear garbage: | ||
| - | {{:intro:antorb1b.png|}} projected on random coordinates (first Fourier modes) until he relented and plotted the unstable manifold of the "upper branch," | + | {{chaosbook:intro:antorb1b.png|}} projected on random coordinates (first Fourier modes) until he relented and plotted the unstable manifold of the "upper branch," |
| - | {{:intro:ant5man12.png|}} and relented even further and plotted the <latex>D_1</latex> discrete symmetry quotiented return map: | + | {{chaosbook:intro:ant5man12.png|}} and relented even further and plotted the <latex>D_1</latex> discrete symmetry quotiented return map: |
| - | {{:intro:ant5mmppf.png|}} And - (the mystery hidden from human eye by being written in the ChaosBook!) - very many periodic orbits followed, labeled by a ternary alphabet. | + | {{chaosbook:intro:ant5mmppf.png|}} And - (the mystery hidden from human eye by being written in the ChaosBook!) - very many periodic orbits followed, labeled by a ternary alphabet. |
| So I know you can do it, if you get your mind to it. | So I know you can do it, if you get your mind to it. | ||
chaosbook/maps.txt · Last modified: 2014/12/03 09:14 by predrag
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