<- [[:chaosbook]] ====== Chapter: Fixed points, and how to get them ====== (ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#cycles|Fixed points, and how to get them]]) --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2010-04-09// enter the latest posts at the bottom of a section - flows better:
to find recent edits: click on [Recent changes], select changed page, then [Old revision], compare versions ===== Blog ===== **2010-05-24 François Mauger** //(mauger snail cpt point univ-mrspint point fr)// For understanding the atomic systems we are dealing with, with T. Uzer and C. Chandre, we have been looking for periodic orbits. We have been using probabilistic metaheuristic algorithm such as the Simulated Annealing to do that. Are you aware of methods based on stochastic algorithms to find periodic orbits for Hamiltonian systems or other deterministic flows? **2010-06-10 Predrag to François** We have not used any stochastic algorithms to find periodic orbits. We use methods described in chapters [[http://chaosbook.org/paper.shtml#cycles|13 Fixed points, and how to get them]] and [[http://chaosbook.org/paper.shtml#relax|29 Relaxation for cyclists]], and sometimes we use nearest recurrences for initial guesses, as for example in [[http://chaosbook.org/tutorials/recurr.html|http://chaosbook.org/tutorials/recurr.html]]. Is this helpful? If not, you can skype me - might be faster than emails (my [[http://www.cns.gatech.edu/%7Epredrag/schedule/travel.txt|schedule]]) ===== Section: Cycles found by thinking ===== Read Morita, Y. and Fujiwara, N. and Kobayashi, M. U. and Mizuguchi, T., "Scytale decodes chaos: A method for estimating unstable symmetric solutions", //Chaos// **20**, 013126 (2010). They say: "A method for estimating a period of unstable periodic solutions is suggested in continuous dissipative chaotic dynamical systems. The measurement of a minimum distance between a reference state and an image of transformation of it exhibits a characteristic structure of the system, and the local minima of the structure give candidates of period and state of corresponding symmetric solutions. Appropriate periods and initial states for the Newton method are chosen efficiently by setting a threshold to the range of the minimum distance and the period." **2010-03-12 PC** I have studied the paper - see repository siminos/blog/dailBlog.tex for my notes. ~~DISCUSSION~~