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Continuum-wise expansivity and entropy for flows

  • ALEXANDER ARBIETO (a1), WELINGTON CORDEIRO (a2) and MARIA JOSÉ PACIFICO (a1)

Abstract

We define the concept of continuum-wise expansivity for flows, and we prove that continuum-wise expansive flows on compact metric spaces with topological dimension greater than one have positive entropy.

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[B1] Bowen, R.. Entropy for group endomorphisms and homogeneous spaces. Trans. Amer. Math. Soc. 153 (1970), 401414.
[B2] Bowen, R.. Periodic orbits for hyperbolic flows. Amer. J. Math. 94 (1972), 130.
[B3] Bowen, R.. Entropy-expansive maps. Trans. Amer. Math. Soc. 164 (1972), 323331.
[BW] Bowen, R. and Walters, P.. Expansive one-parameter flows. J. Differ. Equations 12 (1972), 180193.
[Ft] Fathi, A.. Expansiveness, hyperbolicity and Hausdorff dimension. Commun. Math. Phys. 126 (1989), 249262.
[Hi] Hiraide, K.. Expansive homeomorphisms with the pseudo-orbit tracing property of n-tori. J. Math. Soc. Japan 41(3) (1989), 357389.
[Hi2] Hiraide, K.. Expansive homeomorphisms of compact surfaces are pseudo-Anosov. Osaka J. Math. 63(9) (1987), 337338.
[Ka] Kato, H.. Continuum-wise expansive homeomorphisms. Canadian J. Math. 45(3) (1993), 576598.
[KS] Keynes, H. B. and Sears, M.. Real-expansive flows and topological dimension. Ergod. Th. & Dynam. Sys. 1 (1981), 179195.
[Le1] Lewowicz, J.. Persistence in expansive systems. Ergod. Th. & Dynam. Sys. 3 (1983), 567578.
[Le2] Lewowicz, J.. Expansive homeomorphisms on surfaces. Bol. Soc. Bras. Mat. 20(1) (1989), 113133.
[Ma] Mañé, R.. Expansive homeomorphisms and topological dimension. Trans. Amer. Math. Soc. 252 (1979), 313319.
[N] Nadler, S. B. Jr. Hyperspaces of Sets (Pure and Applied Mathematics, 49) . Dekker, New York, 1978.
[Re] Reddy, W. L.. Pointwise expansion homeomorphisms. J. Lond. Math. Soc. (2) 2 (1970), 232236.
[Sc] Schwartzman, S.. On transformations groups. PhD Dissertation, Yale University, 1952.
[T] Thomas, R. F.. Topological entropy of fixed-point free flows. Trans. Amer. Math. Soc. 319(2) (1990), 601618.
[Ut] Utz, W. R.. Unstable homeomorphisms. Proc. Amer. Math. Soc. 1(6) (1950), 769774.
[Vi] Vieitez, J.. Lyapunov functions and expansive diffeomorphisms on 3D-manifolds. Ergod. Th. & Dynam. Sys. 22(2) (2002), 601632.

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