On specification and measure expansiveness

Welington Cordeiro; Manfred Denker; Xuan Zhang

doi:10.3934/dcds.2017082

Article Contents

2017, Volume 37, Issue 4: 1941-1957. Doi: 10.3934/dcds.2017082

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On specification and measure expansiveness

1.
Department of Mathematics, Universidade Federal do Rio de Janeiro, Rio de Janeiro, CEP 21941-909 RJ, Brazil
2.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA

Received: May 31, 2016

Revised: October 31, 2016

Published: May 2017

The research of W.C. was supported by CAPES and CNPq, and of M.D. by Johann-Gottfried-Herder Foundation.

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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.

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Mathematics Subject Classification: Primary:37B99;Secondary:37D99.

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References

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