This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. L. Adler and B. Weiss. Entropy, a complete metric invariant for automorphisms of the torus, Proc. Natl. Acad. Sci. 57
R. Bowen. Markov partitions for Axiom A diffeomorphisms, Amer. J. Math. 92 (1970), 725–747.
_____. Markov partitions and minimal sets for Axiom A diffeomorphisms, Amer. J. Math. 94 (1970), 907–918.
_____. Periodic orbits for hyperbolic flows, Amer. J. Math.
_____. One-dimensional hyperbolic sets for flows, Jour. Diff. Eqns.
_____. Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc. 154 (1971), 377–397.
_____. Maximizing entropy for a hyperbolic flow, Math. Systems Theory.
R. Bowen and O. E. Lanford. Zeta functions of restrictions of the shift transformation, Proc. Symp. Pure Math., Vol. 14 (1970), 43–49.
L. W. Goodwyn. Topological entropy bounds measure theoretic entropy, Proc. Amer. Math. Soc. 23 (1969), 679–688.
J. Guckenheimer. Axiom A and nocycles imply ζ f (t) rational, Bull. Amer. Math. Soc. 76 (1970), 592–594.
J. Hadamard. Les surfaces a courbures opposees e leur liques geodesiques, Jr. Math. Pures Appl. 4 (1898), 27–73.
G. A. Hedlund. Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory, 3 (1969), 320–375.
G. A. Hedlund and M. Morse. Symbolic dynamics, Amer. J. Math. 69 (1938), 815–866.
A. Manning. Axiom A diffeomorphisms have rational zeta functions, functions, Bull. London Math. Soc. 3 (1971), 215–220.
M. Morse. Representation of geodesics, Amer. J. Math. 43 (1921), 33–51.
_____. Recurrent geodesics on a surface of negative curvature, Trans. Amer. Math. Soc. 22 (1921), 84–110.
_____. Symbolic dynamics, lecture notes, Institute for Advanced Study, Princeton.
N. Friedman and D. Ornstein, On isomorphism of weak Bernoulli transformations, Advances in Math. 5(1970), 365–394.
W. Parry. Intrinsic Markov chains, Trans. Amer. Math. Soc. 112 (1964), 55–66.
Ya. G. Sinai. Markov partitions and C-diffeomorphisms, Func. Anal. and its Appl. 2 (1968), no. 1, 64–89.
S. Smale. Diffeomorphisms with many periodic points, "Differential and Combinatorial Topology", Princeton 1965, 63–80.
_____. Differentiable Dynamical Systems, Bull. Amer. Math. Soc. 73 (1967), 747–817.
R. Bowen. Topological entropy and Axiom A, Proc. Symp. Pure Math., Vol. 14 (1970), 23–41.
_____. Symbolic dynamics for hyperbolic flows, Amer. J. Math.
D. Ruelle, Statistical mechanics on a compact set with Z v action satisfying expansiveness and specification.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1973 Springer-Verlag
About this paper
Cite this paper
Bowen, R. (1973). Symbolic dynamics for hyperbolic systems. In: Beck, A. (eds) Recent Advances in Topological Dynamics. Lecture Notes in Mathematics, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061722
Download citation
DOI: https://doi.org/10.1007/BFb0061722
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06187-8
Online ISBN: 978-3-540-38414-4
eBook Packages: Springer Book Archive