Shadowing is generic---a continuous map case

Piotr Kościelniak; Marcin Mazur; Piotr Oprocha; Paweł Pilarczyk

doi:10.3934/dcds.2014.34.3591

Article Contents

2014, Volume 34, Issue 9: 3591-3609. Doi: 10.3934/dcds.2014.34.3591

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Shadowing is generic---a continuous map case

1.
Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics, Department of Applied Mathematics, ul. Łojasiewicza 6, 30-348 Kraków
2.
Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków
3.
Centre of Mathematics, University of Minho, Campus de Gualtar, 4710-057 Braga

Received: December 31, 2012

Revised: November 30, 2013

Published: August 2014

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Abstract

We prove that shadowing (the pseudo-orbit tracing property), periodic shadowing (tracing periodic pseudo-orbits with periodic real trajectories), and inverse shadowing with respect to certain families of methods (tracing all real orbits of the system with pseudo-orbits generated by arbitrary methods from these families) are all generic in the class of continuous maps and in the class of continuous onto maps on compact topological manifolds (with or without boundary) that admit a decomposition (including triangulable manifolds and manifolds with handlebody).

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Mathematics Subject Classification: 37C50, 37C20, 54H20, 37B99.

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