Shadowing is generic on dendrites

Will Brian; Jonathan Meddaugh; Brian Raines

doi:10.3934/dcdss.2019142

Article Contents

2019, Volume 12, Issue 8: 2211-2220. Doi: 10.3934/dcdss.2019142

This issue Previous Article Special issue on fractal geometry, dynamical systems, and their applications Next Article Free probability on

$ C^{*}$

-algebras induced by hecke algebras over primes

Shadowing is generic on dendrites

1.
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA
2.
Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA

* Corresponding author: Will Brian
* Corresponding author: Will Brian

Received: July 31, 2016

Revised: November 30, 2016

Published: December 2019

The second author gratefully acknowledge support from the European Union through funding the H2020-MSCA-IF-2014 project ShadOmIC (SEP-210195797)

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Abstract

We show that shadowing is a generic property for continuous maps on dendrites.

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Mathematics Subject Classification: 37B50, 37B10, 37B20, 54H20.

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References

[1]	D. V. Anosov, Geodesic Flows on Closed Riemann Manifolds with Negative Curvature, Proceedings of the Steklov Institute of Mathematics, 90 (1967). Translated from the Russian by S. Feder, American Mathematical Society, Providence, R. I., 1969.
[2]	N. C. Bernardes and U. B. Darji, Graph-theoretic structure of maps of the Cantor space, Advances in Mathematics, 231 (2012), 1655-1680. doi: 10.1016/j.aim.2012.05.024.
[3]	R. E. Bowen, $ \omega$-limit sets for axiom A diffeomorphisms, Journal of Differential Equations, 18 (1975), 333-339. doi: 10.1016/0022-0396(75)90065-0.
[4]	L. Carleson and T. W. Gamelin, Complex Dynamics, Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993. doi: 10.1007/978-1-4612-4364-9.
[5]	R. M. Corless and S. Yu. Pilyugin, Approximate and real trajectories for generic dynamical systems, Journal of Mathematical Analysis and Applications, 189 (1995), 409-423. doi: 10.1006/jmaa.1995.1027.
[6]	P. Kościelniak, M. Mazur, P. Oprocha and P. Pilarczyk, Shadowing is generic-a continuous map case, Discrete and Continuous Dynamical Systems, 34 (2014), 3591-3609. doi: 10.3934/dcds.2014.34.3591.
[7]	M. Mazur, Weak shadowing for discrete dynamical systems on nonsmooth manifolds, Journal of Mathematical Analysis and Applications, 281 (2003), 657-662. doi: 10.1016/S0022-247X(03)00186-0.
[8]	M. Mazur and P. Oprocha, $ S$-limit shadowing is $ C^0$-dense, Journal of Mathematical Analysis and Applications, 408 (2013), 465-475. doi: 10.1016/j.jmaa.2013.06.004.
[9]	I. Mizera, Generic properties of one-dimensional dynamical systems, in Ergodic Theory and Related Topics III, volume 1514 of Lecture Notes in Mathematics, Springer, Berlin, (1992), 163-173. doi: 10.1007/BFb0097537.
[10]	K. Odani, Generic homeomorphisms have the pseudo-orbit tracing property, Proceedings of the American Mathematical Society, 110 (1990), 281-284. doi: 10.1090/S0002-9939-1990-1009998-8.
[11]	S. Yu. Pilyugin and O. B. Plamenevskaya, Shadowing is generic, Topology and Its Applications, 97 (1999), 253-266. doi: 10.1016/S0166-8641(98)00062-5.
[12]	K. Yano, Generic homeomorphisms of $ S^1$ have the pseudo-orbit tracing property, Journal of the Faculty of Science, University of Tokyo, Section IA: Mathematics, 34 (1987), 51-55.