Computing Invariant Densities and Metric Entropy
Copyright policy )Computing Invariant Densities and Metric Entropy
This paper deals with the absolutely continuous invariant measure \(\mu\) for a piecewise analytic expanding Markov map \(T\) of the interval. The authors present a method for accurately computing the Lyapunov exponent of \(\mu\). The authors construct atomic signed measures \(\mu_M\) supported on periodic orbits up to period \(M\), and prove that \(\int\log|T'|d\mu_M\to h(\mu)\) super-exponentially fast. Moreover they provide numerous examples.
- University of Manchester United Kingdom
- Centre national de la recherche scientifique France
- University of Manchester United Kingdom
Dynamical systems involving maps of the interval, invariant measure, Dynamical aspects of measure-preserving transformations, periodic orbit, expanding map, Entropy and other invariants, isomorphism, classification in ergodic theory, Markov maps, Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
Dynamical systems involving maps of the interval, invariant measure, Dynamical aspects of measure-preserving transformations, periodic orbit, expanding map, Entropy and other invariants, isomorphism, classification in ergodic theory, Markov maps, Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
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