A dynamical theory for singular stochastic delay differential equations Ⅱ: nonlinear equations and invariant manifolds

Mazyar Ghani Varzaneh; Sebastian Riedel

doi:10.3934/dcdsb.2020304

Article Contents

2021, Volume 26, Issue 8: 4587-4612. Doi: 10.3934/dcdsb.2020304

This issue Previous Article Time periodic solutions for a two-species chemotaxis-Navier-Stokes system Next Article

A dynamical theory for singular stochastic delay differential equations Ⅱ: nonlinear equations and invariant manifolds

Mazyar Ghani Varzaneh^1,2, and
Sebastian Riedel^1,3, ,

1.
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
2.
Sharif University of Technology, Azadi Ave, Tehran, Iran
3.
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Germany

^* Corresponding author: Sebastian Riedel
^* Corresponding author: Sebastian Riedel

Received: February 29, 2020

Early access: October 2020

Published: August 2021

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Abstract

Building on results obtained in [21], we prove Local Stable and Unstable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rough paths theory and a semi-invertible Multiplicative Ergodic Theorem for cocycles acting on measurable fields of Banach spaces obtained in [20].

Keywords:

Random dynamical systems,
rough paths,
stable and unstable manifolds,
stochastic delay differential equations.

Mathematics Subject Classification: Primary:60H20, 60L20;Secondary:34K19, 34K50, 37D10, 37H15.

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References

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