A SHADOWING LEMMA FOR RANDOM DYNAMICAL SYSTEMS

Siyu Gao

doi:10.11948/20210100

2021 Volume 11 Issue 6

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Siyu Gao. A SHADOWING LEMMA FOR RANDOM DYNAMICAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 3014-3030. doi: 10.11948/20210100

Citation:

Siyu Gao. A SHADOWING LEMMA FOR RANDOM DYNAMICAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 3014-3030. doi: 10.11948/20210100

A SHADOWING LEMMA FOR RANDOM DYNAMICAL SYSTEMS

Siyu Gao^1, ,

1.
College of Mathematics, Jilin University, Changchun, 130012, China

Corresponding author: Email address: siyugao@yahoo.com(S. Gao)

Abstract

Abstract

This paper proves a shadowing lemma for the random dynamical systems generated by a class of random parabolic equations. We propose random versions of Newton's method and solution-tracing theory to obtain our main theorem. This result applies to C¹ random dynamical systems on Banach space without assuming the corresponding map to be a diffeomorphism. We also provide sufficient conditions to assure the measurability of the resulting solution. This measurability can be verified as long as a proper subsequence of the initial iteration sequence is measurable.
- Shadowing lemma /
- random dynamical system /
- hyperbolic set
MSC: 37H05, 37C50

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