On averaged tracing of periodic average pseudo orbits

Piotr Oprocha; Xinxing Wu

doi:10.3934/dcds.2017212

Article Contents

2017, Volume 37, Issue 9: 4943-4957. Doi: 10.3934/dcds.2017212

This issue Previous Article Hyperbolic sets that are not contained in a locally maximal one Next Article Fiber bunching and cohomology for Banach cocycles over hyperbolic systems

On averaged tracing of periodic average pseudo orbits

Piotr Oprocha^1,2, and
Xinxing Wu^3,4, ,

1.
Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
2.
National Supercomputing Centre IT4Innovations, Division of the University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22,70103 Ostrava, Czech Republic
3.
School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, China
4.
Institute of Nonlinear Dynamics, Southwest Petroleum University, Chengdu, Sichuan 610500, China

* Corresponding author: Xinxing Wu
* Corresponding author: Xinxing Wu

Received: June 2016

Revised: April 2017

Published: October 2017

Research of P. Oprocha was partly supported by the project "LQ1602 IT4Innovations excellence in science" and by AGH local grant. Research of X. Wu was supported by the National Natural Science Foundation of China (No. 11601449) and the scientific research starting project of Southwest Petroleum University (No. 2015QHZ029)

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Abstract

We propose a definition of average tracing of finite pseudo-orbits and show that in the case of this definition measure center has the same property as nonwandering set for the classical shadowing property. We also show that the average shadowing property trivializes in the case of mean equicontinuous systems, and that it implies distributional chaos when measure center is nondegenerate.

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Mathematics Subject Classification: Primary: 37B05; Secondary: 54H20, 37B20, 37D45, 37C50.

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