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PubMed2002

Chaotic maps derived from trajectory data.

We assume that we have the following information from observed trajectory data about a discrete time dynamical process: (1) a rough graph of the phase plot, (2) the probability density function and (3) the metric entropy. We describe a method for constructing a nonlinear map whose graph is "within" the rough graph of the phase plot, and which has the observed probability density function and entropy.(c) 2002 American Institute of Physics.

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PubMed1995

Iterated function systems and dynamical systems.

We study the relationship between measures invariant for a piecewise expanding transformation tau of a compact metric space endowed with a underlying measure and measures invariant for an iterated function system T(tau), generated by inverse branches of tau. The main result says that the tau-invariant absolutely continuous measure &mgr; is also T(tau) invariant if and only if tau is absolutely continuously conjugated with a piecewise linear transformation. Measures of maximal entropy and general equilibrium states are also discussed. (c) 1995 American Institute of Physics.

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