Unstable manifolds for rough evolution equations

Hongyan Ma; Hongjun Gao

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arXiv · 2209.12217

Unstable manifolds for rough evolution equations

Hongyan Ma·Hongjun Gao

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Abstract

In this paper, we consider a class of evolution equations driven by finite-dimensional $\gamma$-H\"{o}lder rough paths, where $\gamma\in(1/3,1/2]$. We prove the global-in-time solutions of rough evolution equations(REEs) in a sutiable space, also obtain that the solutions generate random dynamical systems. Meanwhile, we derive the existence of local unstable manifolds for such equations by a properly discretized Lyapunov-Perron method.

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Hongyan Ma, Hongjun Gao. 2022-09-25. Unstable manifolds for rough evolution equations. https://arxiv.org/abs/2209.12217

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