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<- [[: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//

===== Blog =====


===== 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."


~~DISCUSSION~~

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