On a shadowing lemma in metric spaces. (English) Zbl 0808.54028

Žáčik, Tibor

Math. Bohem. 117, No. 2, 137-149 (1992).

Summary: Conditions are studied, under which a pseudo-orbit of a continuous map \(f : M \to M\), where \(M\) is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map \(f\).

MSC:

54H20	Topological dynamics (MSC2010)
37B99	Topological dynamics
37D99	Dynamical systems with hyperbolic behavior
54C30	Real-valued functions in general topology
54E35	Metric spaces, metrizability

Keywords:

shadowing property; shadowing lemma; pseudo-orbit