Various shadowing properties for positively expansive maps

By Kazuhiro Sakai. 2003

87 citations recorded by the source corpus.

Abstract In this paper, various shadowing properties are considered for a positively expansive map on a compact metrizable space. We show that the Lipschitz shadowing property, the s -limit shadowing property and the strong shadowing property are all equivalent to the (usual) shadowing property for a positively expansive map. Furthermore, for a positively expansive open map, the average shadowing property is shown.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a4138ea37b5eb2ad7906ff3f21d610b1ae618cb0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Piotr Oprocha
2. Dominik Kwietniak
3. Jonathan Meddaugh
4. A. Barwell
5. Brian E. Raines
6. Marcin Kulczycki

In Mathematical Physics

1. Dominik Kwietniak
2. Piotr Oprocha
3. Jonathan Meddaugh
4. A. Barwell
5. Brian E. Raines
6. Marcin Kulczycki

Citations in the corpus

• On almost specification and average shadowing properties (2013, background): “The notion gained considerable attention of the scientific community, see [4, 5, 6, 7, 23, 30, 31, 32, 35].”
• Shadowing and $\omega $-limit sets of circular Julia sets (2011, methodology): “Many authors refer to maps which are expanding on the whole space [17, 22, 23, 24]; there are many situations however where a map will be expanding only in a local sense i.”