Nonsmooth mappings with Lipschitz shadowing
A. Petrov, S. Pilyugin
TL;DR
This paper investigates conditions for Lipschitz shadowing in nonsmooth, piecewise affine mappings and demonstrates the existence of a homeomorphism with a nonisolated fixed point that possesses this property.
Contribution
It provides new conditions for Lipschitz shadowing in nonsmooth systems and constructs an example of a homeomorphism with a nonisolated fixed point exhibiting this property.
Findings
Established conditions for Lipschitz shadowing in piecewise affine mappings
Constructed a homeomorphism with a nonisolated fixed point that has Lipschitz shadowing
Extended understanding of shadowing properties in nonsmooth dynamical systems
Abstract
We study conditions under which a piecewise affine mapping has the Lipschitz shadowing property. As an application, we show that there exists a homeomorphism with a nonisolated fixed point having the Lipschitz shadowing property.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation