On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems

Doan Thai Son

doi:10.3934/dcdsb.2017166

Article Contents

2017, Volume 22, Issue 8: 3113-3126. Doi: 10.3934/dcdsb.2017166

This issue Previous Article Limit cycles for regularized discontinuous dynamical systems with a hyperplane of discontinuity Next Article Dichotomy and periodic solutions to partial functional differential equations

On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems

Doan Thai Son^1,2,

1.
Institute of Mathematics, Vietnam Academy of Science and Technology, Viet Nam
2.
Department of Mathematics, Hokkaido University, Japan

Received: March 2016

Revised: December 2016

Published: October 2017

This work is supported by the JSPS International Fellowship for Research in Japan (P15320).

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Abstract

In this paper, we construct an open and dense set in the space of bounded linear random dynamical systems (both discrete and continuous time) equipped with the essential sup norm such that the Lyapunov exponents depend analytically on the coefficients in this set. As a consequence, analyticity for Lyapunov exponents of bounded linear random dynamical systems is a generic property.

Keywords:

Lyapunov exponents,
random dynamical systems.

Mathematics Subject Classification: 37H15.

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References

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