Saddles for expansive flows with the pseudo orbits tracing property

Ombach, Jerzy

doi:10.4064/ap-56-1-37-48

Ann. Polon. Math.

1991

DOI: 10.4064/ap-56-1-37-48

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Saddles for expansive flows with the pseudo orbits tracing property

Jerzy Ombach

Abstract: Let F be an expansive flow with the pseudo orbits tracing property on a compact metric space X. Suppose X is connected, locally connected and contains at least two distinct orbits. Then any point is a saddle.

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1996

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Shadowing, expansiveness and hyperbolic homeomorphisms

Ombach¹

1996

J Aust Math Soc A

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The purpose of this paper is to complete results concerning the class 3tf of expansive homeomorphisms having the pseudo orbits tracing property on a compact metric space. We show that hyperbolic homeomorphisms introduced by Marte in [8] are exactly those in the class 3^\ then by the result of [12,20] they form a class equal to the Smale space introduced by Ruelle in [18]. Next, assuming that the phase space is a smooth manifold, we show that a diffeomorphism is Anosov if and only if it is in the class £P and is a lower semi-continuity point of the map which assigns to any diffeomorphism the supremum of its expansive constants (possibly zero). Then we discuss the behavior of the dynamical systems generated by homeomorphisms from 3te near their basic sets.

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Shadowing, expansiveness and hyperbolic homeomorphisms

Ombach¹

1996

J Aust Math Soc A

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Saddles for expansive flows with the pseudo orbits tracing property

Abstract: Let F be an expansive flow with the pseudo orbits tracing property on a compact metric space X. Suppose X is connected, locally connected and contains at least two distinct orbits. Then any point is a saddle.

Cited by 1 publication

References 12 publications

Shadowing, expansiveness and hyperbolic homeomorphisms

Shadowing, expansiveness and hyperbolic homeomorphisms

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