Multishadowing in topological dynamics

Abstract

An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small errors contains at least one subsequence that can be shadowed by a subsequence of an exact trajectory with same indices. We study systems with so-called multishadowing property that is any pseudotrajectory can be shadowed by a finite number of exact orbits. Criteria for existence of $\epsilon$-- networks whose iterations are $\epsilon$ -- networks are given. Relations between multishadowing and some ergodic and topological properties of dynamical systems are discussed.

24 pages, 4 figures

References in corpus (2)

• On the interplay between measurable and topological dynamics
• Graph Theoretic Structure of Maps of the Cantor Space