Invariant manifolds and foliations for random differential equations driven by colored noise

Jun Shen; Kening Lu; Bixiang Wang

doi:10.3934/dcds.2020276

Article Contents

2020, Volume 40, Issue 11: 6201-6246. Doi: 10.3934/dcds.2020276

This issue Previous Article Gromov-Hausdorff distances for dynamical systems Next Article The focusing logarithmic Schrödinger equation: Analysis of breathers and nonlinear superposition

Invariant manifolds and foliations for random differential equations driven by colored noise

1.
School of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2.
Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA
3.
Department of Mathematics New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

^* Corresponding author: Kening Lu, klu@math.byu.edu
^* Corresponding author: Kening Lu, klu@math.byu.edu

Received: September 30, 2019

Revised: April 30, 2020

Published: July 2020

This work was supported by NSFC (11501549, 11831012, 11331007, 11971330), NSF (1413603), the Fundamental Research Funds for the Central Universities (YJ201646) and International Visiting Program for Excellent Young Scholars of SCU

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Abstract

In this paper, we prove the existence of local stable and unstable invariant manifolds for a class of random differential equations driven by nonlinear colored noise defined in a fractional power of a separable Banach space. In the case of linear noise, we show the pathwise convergence of these random invariant manifolds as well as invariant foliations as the correlation time of the colored noise approaches zero.

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Mathematics Subject Classification: Primary: 60H15; Secondary: 37H10, 37L55, 37D10.

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