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A stochastic analogue of a theorem of Boyle's on almost flow equivalence

Published online by Cambridge University Press:  19 September 2008

Paulo Ventura Araújo
Paulo Ventura Araújo
Affiliation:
Centro de Matemática, Faculdade de Ciências, 4000 Porto, Portugal
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Abstract

We study a new topological classification of suspension flows on subshifts of finite type, and obtain a new proof of a theorem of Boyle's which states that, in an appropriate sense, all such flows are alike. We prove that the stochastic version of this classification is non-trivial by exhibiting a certain invariant, and show that this invariant is complete in a particular case, although not in general. Symbolic flows are important as models of basic sets of Axiom A flows, and so we discuss the significance of our results for this latter type of flow.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 3 , September 1993 , pp. 417 - 444
Copyright
Copyright © Cambridge University Press 1993

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References

REFERENCES

[A]Abramov, L. M.. On the entropy of a flow. Dokl. Akad. Nauk. SSSR 128 (1959), 647–650.Google Scholar
[AM]Adler, R. L. & Marcus, B.. Topological entropy and equivalence of dynamical systems. Mem. Amer. Math. Soc. 219 (1979).Google Scholar
[B1]Bowen, R.. Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95 (1973), 429–460.CrossRefGoogle Scholar
[B2]Bowen, R.. Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Springer Lecture Notes in Mathematics 470. Springer: Berlin, 1975.Google Scholar
[B3]Boyle, M.. Almost flow equivalence for hyperbolic basic sets. Topology 31 (1992), 857–864.CrossRefGoogle Scholar
[F]Franks, J.. How equivalence of subshifts of finite type. Ergod. Th. & Dynam. Sys. 4 (1984), 53–66.CrossRefGoogle Scholar
[K1]Krieger, W.. On the finitary isomorphisms of Markov shifts that have finite-expected coding time. Z. Wahr. 65 (1977), 323–328.CrossRefGoogle Scholar
[K2]Krieger, W.. On the subsystems of topological Markov chains. Ergod. Th. & Dynam. Sys. 2 (1982), 195–202.CrossRefGoogle Scholar
[L]Lind, D.. The entropies of topological Markov shifts and a related class of algebraic integers, Ergod. Th. & Dynam. Sys. 6 (1986), 571–582.CrossRefGoogle Scholar
[MT]Marcus, B. & Tuncel, S.. The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains. Ergod. Th. & Dynam. Sys. 11 (1991), 129–180.CrossRefGoogle Scholar
[N]Newman, M.., Integral Matrices. Academic: New York, 1972.Google Scholar
[P]Parry, W.. Intrinsic Markov chains. Trans. Amer. Math. Soc. 112 (1964), 55–65.CrossRefGoogle Scholar
[PSc]Parry, W. & Schmidt, K.. Natural coefficients and invariants for Markov chains. Invent. Math. 76 (1984), 15–32.CrossRefGoogle Scholar
[PSu]Parry, W. & Sullivan, D.. A topological invariant for flows on one-dimensional spaces. Topology 14 (1975), 297–299.CrossRefGoogle Scholar
[PT1]Parry, W. & Tuncel, S.. On the stochastic and topological structure of Markov chains. Bull. London Math. Soc. 14 (1982), 16–27.CrossRefGoogle Scholar
[PT2]Parry, W. & Tuncel, S.. Classification problems in Ergodic Theory. London Mathematical Society Lecture Note Series 67. Cambridge University Press: Cambridge, 1982.Google Scholar
[Pe]Petersen, K.. Chains, entropy, coding. Ergod. Th. & Dynam. Sys. 6 (1986), 415–448.CrossRefGoogle Scholar
[R]Ruelle, D.. Thermodynamic formalism. Encyclopedia of Mathematics and its Applications, vol. 5. Addison-Wesley: Reading, MA, 1978.Google Scholar