Pesin's Formula for Random Dynamical Systems on $R^d$

Abstract

Pesin's formula relates the entropy of a dynamical system with its positive Lyapunov exponents. It is well known, that this formula holds true for random dynamical systems on a compact Riemannian manifold with invariant probability measure which is absolutely continuous with respect to the Lebesgue measure. We will show that this formula remains true for random dynamical systems on $R^d$ which have an invariant probability measure absolutely continuous to the Lebesgue measure on $R^d$. Finally we will show that a broad class of stochastic flows on $R^d$ of a Kunita type satisfies Pesin's formula.

35 pages

References in corpus (1)

• Absolute Continuity Theorem for Random Dynamical Systems on $R^d$

Cited by in corpus (2)

• A Random Dynamical Systems Perspective on Isochronicity for Stochastic Oscillations
• Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise