On specification and measure expansiveness

Welington Cordeiro; Manfred Denker; Xuan Zhang

doi:10.3934/dcds.2017082

On specification and measure expansiveness

Welington Cordeiro, Manfred Denker, Xuan Zhang

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

21 Scopus citations

Abstract

We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is introduced, and an example of a non-expansive systems with the strong measure expansive property is given. Moreover, we find a family of examples with the N-expansive property, which are not strong measure expansive. We finally show a spectral decomposition theorem for strong measure expansive dynamical systems with shadowing.

Original language	English (US)
Pages (from-to)	1941-1957
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	37
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2017082
State	Published - Apr 2017

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2017082

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abstract = "We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is introduced, and an example of a non-expansive systems with the strong measure expansive property is given. Moreover, we find a family of examples with the N-expansive property, which are not strong measure expansive. We finally show a spectral decomposition theorem for strong measure expansive dynamical systems with shadowing.",

author = "Welington Cordeiro and Manfred Denker and Xuan Zhang",

note = "Funding Information: The research of W.C. was supported by CAPES and CNPq, and of M.D. by Johann-Gottfried-Herder Foundation.",

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AU - Denker, Manfred

AU - Zhang, Xuan

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N2 - We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is introduced, and an example of a non-expansive systems with the strong measure expansive property is given. Moreover, we find a family of examples with the N-expansive property, which are not strong measure expansive. We finally show a spectral decomposition theorem for strong measure expansive dynamical systems with shadowing.

AB - We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is introduced, and an example of a non-expansive systems with the strong measure expansive property is given. Moreover, we find a family of examples with the N-expansive property, which are not strong measure expansive. We finally show a spectral decomposition theorem for strong measure expansive dynamical systems with shadowing.

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

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On specification and measure expansiveness

Abstract

All Science Journal Classification (ASJC) codes

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