On almost specification and average shadowing properties

By Marcin Kulczycki, Dominik Kwietniak, Piotr Oprocha. 2013

104 citations recorded by the source corpus.

In this paper we study relations between almost specification property, asymptotic average shadowing property and average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples that compactness is a necessary condition for these implications to hold. As a consequence of our methodology we also obtain a proof that limit shadowing in chain transitive systems implies shadowing.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7ef8769bd5ad98fb7b5a848e1dc29d6439148e00

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In Mathematical Physics

1. Dominik Kwietniak
2. Piotr Oprocha
3. Martha Lkacka

Citations in the corpus

• A PANORAMA OF SPECIFICATION-LIKE PROPERTIES AND THEIR CONSEQUENCES (2015, background): “Both follow from the almost specification property (see [45, 93]).”