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Continuum-wise expansivity and entropy for flows

Published online by Cambridge University Press:  28 September 2017

ALEXANDER ARBIETO ,
WELINGTON CORDEIRO  and
MARIA JOSÉ PACIFICO
ALEXANDER ARBIETO
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil email [email protected], [email protected]
WELINGTON CORDEIRO
Affiliation:
IMPA, Estrada Dona Castorina, 110 CEP 22.460, Rio de Janeiro, RJ, Brazil email [email protected]
MARIA JOSÉ PACIFICO
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil email [email protected], [email protected]
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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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 5 , May 2019 , pp. 1190 - 1210
Copyright
© Cambridge University Press, 2017 

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References

Bowen, R.. Entropy for group endomorphisms and homogeneous spaces. Trans. Amer. Math. Soc. 153 (1970), 401–414.Google Scholar
Bowen, R.. Periodic orbits for hyperbolic flows. Amer. J. Math. 94 (1972), 1–30.Google Scholar
Bowen, R.. Entropy-expansive maps. Trans. Amer. Math. Soc. 164 (1972), 323–331.Google Scholar
Bowen, R. and Walters, P.. Expansive one-parameter flows. J. Differ. Equations 12 (1972), 180–193.Google Scholar
Fathi, A.. Expansiveness, hyperbolicity and Hausdorff dimension. Commun. Math. Phys. 126 (1989), 249–262.Google Scholar
Hiraide, K.. Expansive homeomorphisms with the pseudo-orbit tracing property of n-tori. J. Math. Soc. Japan 41(3) (1989), 357–389.Google Scholar
Hiraide, K.. Expansive homeomorphisms of compact surfaces are pseudo-Anosov. Osaka J. Math. 63(9) (1987), 337–338.Google Scholar
Kato, H.. Continuum-wise expansive homeomorphisms. Canadian J. Math. 45(3) (1993), 576–598.Google Scholar
Keynes, H. B. and Sears, M.. Real-expansive flows and topological dimension. Ergod. Th. & Dynam. Sys. 1 (1981), 179–195.Google Scholar
Lewowicz, J.. Persistence in expansive systems. Ergod. Th. & Dynam. Sys. 3 (1983), 567–578.Google Scholar
Lewowicz, J.. Expansive homeomorphisms on surfaces. Bol. Soc. Bras. Mat. 20(1) (1989), 113–133.Google Scholar
Mañé, R.. Expansive homeomorphisms and topological dimension. Trans. Amer. Math. Soc. 252 (1979), 313–319.Google Scholar
Nadler, S. B. Jr. Hyperspaces of Sets (Pure and Applied Mathematics, 49) . Dekker, New York, 1978.Google Scholar
Reddy, W. L.. Pointwise expansion homeomorphisms. J. Lond. Math. Soc. (2) 2 (1970), 232–236.Google Scholar
Schwartzman, S.. On transformations groups. PhD Dissertation, Yale University, 1952.Google Scholar
Thomas, R. F.. Topological entropy of fixed-point free flows. Trans. Amer. Math. Soc. 319(2) (1990), 601–618.Google Scholar
Utz, W. R.. Unstable homeomorphisms. Proc. Amer. Math. Soc. 1(6) (1950), 769–774.Google Scholar
Vieitez, J.. Lyapunov functions and expansive diffeomorphisms on 3D-manifolds. Ergod. Th. & Dynam. Sys. 22(2) (2002), 601–632.Google Scholar