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2019 Random perturbations of hyperbolic dynamics
Florian Dorsch, Hermann Schulz-Baldes
Electron. J. Probab. 24: 1-23 (2019). DOI: 10.1214/19-EJP340

Abstract

A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random perturbations it is shown that the dynamics approaches the stable fixed points of the unperturbed matrix up to errors even if the strength of the perturbation is large compared to the relative increase of nearby diagonal entries of the unperturbed matrix specifying the local hyperbolicity.

Citation

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Florian Dorsch. Hermann Schulz-Baldes. "Random perturbations of hyperbolic dynamics." Electron. J. Probab. 24 1 - 23, 2019. https://doi.org/10.1214/19-EJP340

Information

Received: 5 November 2018; Accepted: 7 July 2019; Published: 2019
First available in Project Euclid: 10 September 2019

zbMATH: 1422.37033
MathSciNet: MR4003142
Digital Object Identifier: 10.1214/19-EJP340

Subjects:
Primary: 37A50, 37H10, 37H15, 60B20

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