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arXiv · 2002.01310

Quasi-shadowing for partially hyperbolic dynamics on Banach spaces

Lucas Backes·Davor Dragicevic
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Abstract

A partially hyperbolic dynamical system is said to have the quasi-shadowing property if every pseudotrajectory can be shadowed by a sequence of points $(x_n)_{n\in \Z}$ such that $x_{n+1}$ is obtained from the image of $x_n$ by moving it by a small factor in the central direction. In the present paper, we prove that a small nonlinear perturbation of a partially dichotomic sequence of (not necessarily invertible) linear operators acting on an arbitrary Banach space has the quasi-shadowing property. We also get obtain a continuous time version of this result. As an application of our main result, we prove that a certain class of partially dichotomic sequences of linear operators is stable up to the movement in the central direction.

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Lucas Backes, Davor Dragicevic. 2020-02-01. Quasi-shadowing for partially hyperbolic dynamics on Banach spaces. https://doi.org/10.1016/j.jmaa.2020.124445

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