×

zbMATH — the first resource for mathematics

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

MSC:
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
28D05 Measure-preserving transformations
PDF BibTeX XML Cite
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
[4] Bowen, R.: Symbolic dynamics for hyperbolic flows. Amer. J. Math.95, 429-459 (1973) · Zbl 0282.58009
[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
[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
[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)
[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
[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
[18] Pugh, C., Shub, M.: The ?-stability theorem for flows. Inventiones math.11, 150-158 (1970) · Zbl 0212.29102
[19] Pugh, C.: Ergodicity of Anosov Actions. Inventiones math.15, 1-23 (1972) · Zbl 0236.58007
[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
[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
[27] Smale, S.: Differentiable dynamical systems. Bull. A.M.S.73, 747-817 (1967) · Zbl 0202.55202
[28] Walters, P.: A variational principle for the pressure of continuous transformations. Amer. J. Math. To appear · Zbl 0318.28007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.