TITLE

An approximation formula and parameter-dependence of statistical quantities in low-dimensional chaotic systems

AUTHOR(S)
Koga, Shinji
PUB. DATE
June 2000
SOURCE
AIP Conference Proceedings;2000, Vol. 519 Issue 1, p365
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We derive an approximation formula for obtaining parameter dependence of statistical quantities in chaotic systems on the basis of a Frobenius-Perron equation. The formula is characterized by three integers; One is the number of application of the Frobenius-Perron operator, the second is the number of the delta-peaks of the initial density, and the third is the number of the integration domains. We find numerically that this formula is applicable to a wide varaiety of states of a system ranging from stable cycles to band-chaos and totaly spread chaotic regime by merely changing the system parameter, except for the very narrow windows representing stable cycles with large periodicity, where the concrete examples are a logistic map, a Hé,non map and so on. We finally consider how we extend our theory to ODE's.
ACCESSION #
5665027

 

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