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Hyperbolic dynamical systems with isolated points

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Geometric Dynamics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1007))

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Abstract

We prove that the non-wandering set of an hyperbolic topologically transitive dynamical system whose basis space is an infinite non perfect set, is the union of two disjoint orbits.

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References

  1. BOWEN, R. "Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms". Lecture Notes in Mathematics, Springer 470 (1975).

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  2. DENKER, M.; GRILLENBERG, C.: SIGMUND, K. "Ergodic Theory on Compact Spaces". Lecture Notes in Mathematics, Springer 527 (1976).

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  3. MARTINEZ, S. "Characterization of Reducible Matrices Defining Topologically Transitive Subshifts". Preprint (1981).

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  4. RUELLE, D. "A measure associated with Axiom A attractors". Amer. Journal of Math. 98 (1976), 619–654.

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J. Palis Jr.

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© 1983 Springer-Verlag

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Servet Martínez, A. (1983). Hyperbolic dynamical systems with isolated points. In: Palis, J. (eds) Geometric Dynamics. Lecture Notes in Mathematics, vol 1007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061434

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  • DOI: https://doi.org/10.1007/BFb0061434

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12336-1

  • Online ISBN: 978-3-540-40969-4

  • eBook Packages: Springer Book Archive

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