Ricardo Ma~n'e, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc. 252 (1979), 313--319. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Expansive Subdynamics - Boyle, Lind (1997) (3 citations) (Correct)
.... homeomorphisms admit hyperbolic metrics [Fr1, R] Expansiveness is also a topological condition: various topological spaces [H2, Ka] for example the 2 sphere, admit no expansive homeomorphism [Lew, H1] and the domain of an expansive homeomorphism must be zero dimensional if it is minimal [Man1] or has zero entropy [Fa] Expansiveness is a finiteness condition: an expansive homeomorphism can only be defined on a finite dimensional space [Man1] an expansive homeomorphism of a compact surface must be pseudo Anosov [Lew, H1] any expansive system is a quotient of a subshift X by a map ....
.... the 2 sphere, admit no expansive homeomorphism [Lew, H1] and the domain of an expansive homeomorphism must be zero dimensional if it is minimal [Man1] or has zero entropy [Fa] Expansiveness is a finiteness condition: an expansive homeomorphism can only be defined on a finite dimensional space [Man1]; an expansive homeomorphism of a compact surface must be pseudo Anosov [Lew, H1] any expansive system is a quotient of a subshift X by a map whose equivalence relation is the intersection of X Theta X with a shift of finite type [Fr4] an expansive system has finite entropy [W, Cor. 7.4.1] and ....
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Ricardo Ma~n'e, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc. 252 (1979), 313--319.
Residual Entropy, Conditional Entropy And Subshift Covers - Boyle, Fiebig, Fiebig (2001) (Correct)
....special case that T is expansive, it is a simple consequence of uniform continuity that any zero dimensional extension S T factors through some subshift extension, S S 0 T . Then the defect of S 0 T is at most that of S T . For T is expansive, it is well known that dim(T ) is nite [Ma1] and Per(T ) is countable ( DGS] Prop. 16.10) Consequently we have the following corollary of Theorem B.1. Corollary B.10. If T is an expansive homeomorphism, then there is a cover : S T such that S is a subshift and has defect zero. RESIDUAL ENTROPY, CONDITIONAL ENTROPY AND SUBSHIFT ....
R. Ma~ne, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc. 252 (1979), 313-319.
Residual Entropy, Conditional Entropy And Subshift Covers - Boyle, Fiebig, Fiebig (2000) (Correct)
....special case that T is expansive, it is a simple consequence of uniform continuity that any zero dimensional extension S T factors through some subshift extension, S S 0 T . Then the defect of S 0 T is at most that of S T . For T is expansive, it is well known that dim(T ) is nite [Ma1] and Per(T ) 28 MIKE BOYLE, DORIS FIEBIG, AND ULF FIEBIG is countable ( DGS] Prop. 16.10) Consequently we have the following corollary of Theorem B.1. Corollary B.10. If T is an expansive homeomorphism, then there is a cover : S T such that S is a subshift and has defect zero. Appendix ....
R. Ma~ne, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc. 252 (1979), 313-319.
Dynamical Constraints on Group Actions - Morris (1998) (1 citation) (Correct)
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R. Ma~n'e, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc. 252 313--319 (1979).
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