Shadowing for induced maps of hyperspaces

Christopher Good; Leobardo Fernández

doi:10.4064/fm136-2-2016

Shadowing for induced maps of hyperspaces

Christopher Good
, Leobardo Fernández

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

459 Downloads (Pure)

Abstract

Given a nonempty compact metric space X and a continuous
function f : X → X, we study shadowing and h-shadowing for
the induced maps on hyperspaces, particularly in symmetric products,
Fn(X), and the hyperspace of compact subsets of X, 2X. We prove
that f has shadowing (h-shadowing) if and only if 2f has shadowing
(h-shadowing).

Original language	English
Pages (from-to)	277-286
Number of pages	10
Journal	Fundamenta Mathematicae
Volume	235
Early online date	4 Jul 2016
DOIs	https://doi.org/10.4064/fm136-2-2016
Publication status	Published - 2016

Keywords

shadowing
pseudo orbit tracing
induced map
hyperspace

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ShadowingInHyper-fund-math-finalAccepted author manuscript, 292 KB

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title = "Shadowing for induced maps of hyperspaces",

abstract = "Given a nonempty compact metric space X and a continuous function f : X → X, we study shadowing and h-shadowing for the induced maps on hyperspaces, particularly in symmetric products, Fn(X), and the hyperspace of compact subsets of X, 2X. We prove that f has shadowing (h-shadowing) if and only if 2f has shadowing (h-shadowing).",

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AU - Good, Christopher

AU - Fernández, Leobardo

PY - 2016

Y1 - 2016

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AB - Given a nonempty compact metric space X and a continuous function f : X → X, we study shadowing and h-shadowing for the induced maps on hyperspaces, particularly in symmetric products, Fn(X), and the hyperspace of compact subsets of X, 2X. We prove that f has shadowing (h-shadowing) if and only if 2f has shadowing (h-shadowing).

KW - shadowing

KW - pseudo orbit tracing

KW - induced map

KW - hyperspace

U2 - 10.4064/fm136-2-2016

DO - 10.4064/fm136-2-2016

M3 - Article

SN - 0016-2736

VL - 235

SP - 277

EP - 286

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

ER -

Shadowing for induced maps of hyperspaces

Abstract

Keywords

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