Preprint A711/2012
SOME CONSEQUENCES OF THE SHADOWING PROPERTY IN LOW DIMENSIONS
Enrique Pujals | Koropecki, Andres
Keywords:
We consider low-dimensional systems with the shadowing prop- erty and we study the problem of existence of periodic orbits. In dimension two, we show that the shadowing property for a homeomorphism implies the existence of periodic orbits in every -transitive class, and in contrast we pro- vide an example of a C ∞ 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-H ̈lder o shadowing property with α > 1/2 implies that the system is conjugate to an expanding map.