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arXiv · 1109.5074

Some Consequences of the Shadowing Property in Low Dimensions

Andres Koropecki·Enrique R. Pujals
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Abstract

We consider low-dimensional systems with the shadowing property. In dimension two, we show that the shadowing property for a homeomorphism implies the existence of periodic orbits in every $ε$-transitive class, and in contrast we provide an example of a $C^\infty$ Kupka-Smale diffeomorphism with the shadowing property exhibiting an aperiodic transitive class. Finally we consider the case of transitive endomorphisms of the circle, and we prove that the $α$-Hölder shadowing property with $α>1/2$ implies that the system is conjugate to an expanding map.

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Andres Koropecki, Enrique R. Pujals. 2012-12-04. Some Consequences of the Shadowing Property in Low Dimensions. https://doi.org/10.1017/etds.2012.195

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