# American Institute of Mathematical Sciences

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April  2020, 40(4): 2267-2283. doi: 10.3934/dcds.2020113

## 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

Received  May 2019 Published  January 2020

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.

Citation: Woochul Jung, Ngocthach Nguyen, Yinong Yang. Spectral decomposition for rescaling expansive flows with rescaled shadowing. Discrete & Continuous Dynamical Systems - A, 2020, 40 (4) : 2267-2283. doi: 10.3934/dcds.2020113
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