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- W1569598210 abstract "Resumo/Abstract: We are concerned with diffeomorphisms which satisfy the shadowing property; i.e. for every > 0 there is δ > 0 such that every δ-pseudo-orbit is -shadowed by a real orbit. This property is typical of hyperbolic systems, in a stronger form. However, little is known about dynamical consequences of the shadowing property by itself, with no additional hypothesis. In particular, does it imply the existence of periodic orbits? We show that if f is a homeomorphism of a compact orientable surface with the shadowing property, then every -transitive class contains a periodic point of f , and thus every chain transitive class is accumulated by periodic points. Additionally, we give an example of a C∞ Kupka-Smale surface diffeomorphism which has the shadowing property but exhibits an aperiodic chain transitive class. We also obtain a stronger result for one-dimensional smooth endomorphisms of the circle assuming a Holder version of the shadowing property." @default.
- W1569598210 created "2016-06-24" @default.
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- W1569598210 date "2011-09-26" @default.
- W1569598210 modified "2023-09-27" @default.
- W1569598210 title "Consequences of the Shadowing Property" @default.
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