Lyapunov functions, shadowing, and topological stability
Alexey A. Petrov, Sergei Yu. Pilyugin
TL;DR
This paper introduces new Lyapunov function-based conditions to determine when a homeomorphism exhibits shadowing and applies these to prove topological stability in certain nonhyperbolic systems.
Contribution
It provides novel Lyapunov function criteria for shadowing and topological stability in nonhyperbolic homeomorphisms on compact metric spaces.
Findings
Established new Lyapunov conditions for shadowing.
Proved topological stability for specific nonhyperbolic homeomorphisms.
Extended stability results beyond hyperbolic dynamics.
Abstract
We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish the topological stability of some homeomorphisms with nonhyperbolic behavior.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Stability and Controllability of Differential Equations