Spectral decomposition for rescaling expansive flows with rescaled shadowing

Woochul Jung; Ngocthach Nguyen; Yinong Yang

doi:10.3934/dcds.2020113

Article Contents

2020, Volume 40, Issue 4: 2267-2283. Doi: 10.3934/dcds.2020113

This issue Previous Article On global smooth solutions of 3-D compressible Euler equations with vanishing density in infinitely expanding balls Next Article A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies

Spectral decomposition for rescaling expansive flows with rescaled shadowing

1.
Department of Mathematics, Chungnam National University, Daejeon 34134, Korea
2.
School of Mathematical Sciences, Beihang University, Beijing 100191, China

^* Corresponding author
^* Corresponding author

Received: April 30, 2019

Published: December 2019

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In this paper, we introduce the concepts of rescaled expansiveness and the rescaled shadowing property for flows on metric spaces which are dynamical properties, and present a spectral decomposition theorem for flows. More precisely, we prove that if a flow is rescaling expansive and has the rescaled shadowing property on a locally compact metric space, then it admits the spectral decomposition. Moreover, we show that if a flow on locally compact metric space has the rescaled shadowing property then its restriction on nonwandering set also has the rescaled shadowing property.

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Mathematics Subject Classification: Primary: 37Bxx; Secondary: 37Dxx.

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