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Bowen, Rufus; Ruelle, David

The ergodic theory of axiom A flows. (English) Zbl 0311.58010

Invent. Math. 29, 181-202 (1975).
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Cited in 14 Reviews
Cited in 367 Documents

MSC:

37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
28D05 Measure-preserving transformations
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Full Text: DOI EuDML

References:

[1] Abramov, L. M.: On the entropy of a flow. A.M.S. Translations49, 167-170 (1966) · Zbl 0185.21803
[2] Bowen, R.: Periodic points and measures for AxiomA diffeomorphisms. Trans. A.M.S.154, 377-397 (1971) · Zbl 0212.29103
[3] Bowen, R.: Periodic orbits for hyperbolic flows. Amer. J. Math.94, 1-30 (1972) · Zbl 0254.58005 · doi:10.2307/2373590
[4] Bowen, R.: Symbolic dynamics for hyperbolic flows. Amer. J. Math.95, 429-459 (1973) · Zbl 0282.58009 · doi:10.2307/2373793
[5] Bowen, R.: Maximizing entropy for a hyperbolic flow. Math. Systems Theory. To appear · Zbl 0303.58014
[6] Bowen, R.: Some systems with unique equilibrium states. Math. Systems Theory. To appear · Zbl 0299.54031
[7] Bowen, R.: Bernoulli equilibrium states for AxiomA diffeomorphisms. Math. Systems Theory. To appear
[8] Bowen, R., Walters, P.: Expansive one-parameter flows. J. Diff. Equs.12, 180-193 (1972) · Zbl 0242.54041 · doi:10.1016/0022-0396(72)90013-7
[9] Bunimovi?, L. A.: Imbedding of Bernoulli shifts in certain special flows (in Russian). Uspehi mat. Nauk28, 171-172 (1973)
[10] Dinaburg, E. I.: On the relations among various entropy characteristics of dynamical systems. Math. USSR Izvestia5, 337-378 (1971) · Zbl 0248.58007 · doi:10.1070/IM1971v005n02ABEH001050
[11] Dobru?in, R. L.: Analyticity of correlation functions in one-dimensional classical systems with slowly decreasing potentials. Commun. math. Phys.32, 269-289 (1973) · doi:10.1007/BF01645609
[12] Gurevi?, B. M.: Some existence conditions forK-decompositions for special flows. Trans. Moscow Math. Soc.17, 99-128 (1967)
[13] Hirsch, M., Palis, J., Pugh, C., Shub, M.: Neighborhoods of hyperbolic sets. Inventiones Math.9, 121-134 (1970) · Zbl 0191.21701 · doi:10.1007/BF01404552
[14] Hirsch, M., Pugh, C.: Stable manifolds and hyperbolic sets. Proc. Symp. in Pure Math.14, 133-163 (1970) · Zbl 0215.53001
[15] Hirsch, M., Pugh, C., Shub, M.: Invariant manifolds. To appear
[16] Liv?ic, A. N., Sinai, Ya. G.: On invariant measures compatible with the smooth structure for transitiveU-systems. Soviet Math. Dokl.13, 1656-1659 (1972) · Zbl 0284.58014
[17] Margulis, G. A.: Certain measures associated withU-flows on compact manifolds. Func. Anal. and its Appl.4, 55-67 (1970) · Zbl 0245.58003 · doi:10.1007/BF01075620
[18] Pugh, C., Shub, M.: The ?-stability theorem for flows. Inventiones math.11, 150-158 (1970) · Zbl 0212.29102 · doi:10.1007/BF01404608
[19] Pugh, C.: Ergodicity of Anosov Actions. Inventiones math.15, 1-23 (1972) · Zbl 0236.58007 · doi:10.1007/BF01418639
[20] Ratner, M.: Anosov flows with Gibbs measures are also Bernoullian. Israel J. Math. To appear · Zbl 0304.28011
[21] Ruelle, D.: Statistical Mechanics. New York: Benjamin 1969 · Zbl 0177.57301
[22] Ruelle, D.: Statistical mechanics of a one-dimensional lattice gas. Commun. Math. Phys.9, 267-278 (1968) · Zbl 0165.29102 · doi:10.1007/BF01654281
[23] Ruelle, D.: Statistical mechanics on a compact set with Zn action satisfying expansiveness and specification. Trans. A.M.S. To appear · Zbl 0255.28015
[24] Ruelle, D.: A measure associated with AxiomA attractors. Amer. J. Math. To appear · Zbl 0355.58010
[25] Sinai, Ya. G.: Markov partitions andY-diffeomorphisms. Func. Anal. and its Appl.2, 64-69 (1968)
[26] Sinai, Ya. G.: Gibbs measures in ergodic theory. Russ. Math. Surveys166, 21-69 (1972) · Zbl 0246.28008 · doi:10.1070/RM1972v027n04ABEH001383
[27] Smale, S.: Differentiable dynamical systems. Bull. A.M.S.73, 747-817 (1967) · Zbl 0202.55202 · doi:10.1090/S0002-9904-1967-11798-1
[28] Walters, P.: A variational principle for the pressure of continuous transformations. Amer. J. Math. To appear · Zbl 0318.28007
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