Synchronization in iterated function systems
Synchronization in iterated function systems
复制标题
迭代函数系统中的同步
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
A. J. Homburg
中科院分区：
文献类型：
--
作者：
A. J. Homburg
本文研究紧流形上迭代函数系统的同步问题，分为两种情况：(i)由具有绝对连续参数噪声的随机微分同态生成的迭代函数系统；（ii）由有限多个微分同态生成的迭代函数系统。
We treat synchronization for iterated function systems on compact manifolds in two cases:(i) iterated function systems generated by random diffeomorphisms with absolutely continuous parametric noise,(ii) iterated function systems generated by finitely many diffeomorphisms.
Synchronization is the convergence of orbits starting at different initial conditions when iterated by the same sequence of diffeomorphisms. The iterated function systems admit a description as skew product systems of diffeomorphisms on compact manifolds driven by shift operators. Under open conditions including transitivity and negative fiber Lyapunov exponents, we prove the existence of a unique attracting invariant graph for the skew product system. This explains the occurrence of synchronization.
For skew product systems arising from iterated function systems generated by finitely many diffeomorphisms we have the following additional statements. Recent work by Bochi, Bonatti and D\'{\i}az establishes the existence of an open class of such skew product systems that admit invariant measures of full support with zero fiber Lyapunov exponents. Our results imply the existence of an open class of skew product systems that simultaneously admit an invariant measure of full support, Bernoulli measure as marginal, and negative fiber Lyapunov exponents.