Estimating invariant measures and Lyapunov exponents
نویسندگان
چکیده
منابع مشابه
Estimating Invariant Measures and Lyapunov Exponents
This paper describes a method for obtaining rigorous numerical bounds on time averages for a class of one-dimensional expanding maps. The idea is to directly estimate the absolutely continuous invariant measure for these maps, without computing trajectories. The main theoretical result is a bound on the convergence rate of the Frobenius-Perron operator for such maps. The method is applied to es...
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We present a method of approximating the unique invariant measure and associated Lyapunov exponents of a random dynamical system deened by the iid composition of a family of maps in situations where only one Lyapunov exponent is observed. As a corollary, our construction also provides a method of estimating the top Lyapunov exponent of an iid random matrix product. We develop rigorous numerical...
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Let M be a compact invariant set contained in a boundary hyperplane of the positive orthant of R for a discrete or continuous time dynamical system defined on the positive orthant. Using elementary arguments, we show that M is uniformly weakly repelling in directions normal to the boundary in which M resides provided all normal Lyapunov exponents are positive. This result is useful in establish...
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Lyapunov exponents of a hyperbolic ergodic measure are approximated by Lyapunov exponents of hyperbolic atomic measures on periodic orbits.
متن کاملLyapunov exponents, dual Lyapunov exponents, and multifractal analysis.
It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of one-dimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps. (c) 1999 American Institute of Physics.
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1996
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s014338570000907x