Expansivity and shadowing in subspaces

Andy D Barwell; Chris Good; Piotr Oprocha

doi:10.4064/fm219-3-2

Expansivity and shadowing in subspaces

Andy D Barwell, Chris Good, Piotr Oprocha

Research output: Contribution to journal › Article (Academic Journal) › peer-review

32 Citations (Scopus)

Abstract

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.

Original language	English
Pages (from-to)	223-243
Number of pages	21
Journal	Fundamenta Mathematicae
Volume	219
Issue number	3
DOIs	https://doi.org/10.4064/fm219-3-2
Publication status	Published - 2013

Keywords

OMEGA-LIMIT SETS
expanding map
interval map
DYNAMICAL-SYSTEMS
shadowing
expansivity
APPROXIMATE
pseudo-orbit tracing
TENT MAPS
expansive map

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title = "Expansivity and shadowing in subspaces",

abstract = "We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.",

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T1 - Expansivity and shadowing in subspaces

AU - Barwell, Andy D

AU - Good, Chris

AU - Oprocha, Piotr

PY - 2013

Y1 - 2013

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AB - We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.

KW - OMEGA-LIMIT SETS

KW - expanding map

KW - interval map

KW - DYNAMICAL-SYSTEMS

KW - shadowing

KW - expansivity

KW - APPROXIMATE

KW - pseudo-orbit tracing

KW - TENT MAPS

KW - expansive map

U2 - 10.4064/fm219-3-2

DO - 10.4064/fm219-3-2

M3 - Article (Academic Journal)

SN - 0016-2736

VL - 219

SP - 223

EP - 243

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 3

ER -

Expansivity and shadowing in subspaces

Abstract

Keywords

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