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

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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  • 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.

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

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