zbMATH — the first resource for mathematics

Unique ergodicity of some flows related to axiom A diffeomorphisms. (English) Zbl 0314.58012

37D99 Dynamical systems with hyperbolic behavior
28D05 Measure-preserving transformations
57R30 Foliations in differential topology; geometric theory
37C75 Stability theory for smooth dynamical systems
Full Text: DOI
[1] R. Bellman,Introduction to Matrix Analysis, 2nd Edition, McGraw-Hill, 1970. · Zbl 0216.06101
[2] R. Bowen,Markov partitions for Axiom A diffeomorphisms, Amer. J. Math.92 (1970), 725–747. · Zbl 0208.25901
[3] R. Bowen,Markov partitions and minimal sets for Axiom A diffeomorphisms, Amer. J. Math.92 (1970), 907–918. · Zbl 0212.29104
[4] R. Bowen,Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc.154 (1971), 377–397. · Zbl 0212.29103
[5] R. Bowen,Equilibrium states and ergodic theory of Anosov diffeomorphisms, lecture notes. · Zbl 0308.28010
[6] J. Franks,Anosov diffeomorphisms, Proc. Symp. Pure Math.14, Amer. Math. Soc., Providence, R. I., 1970, 61–93. · Zbl 0207.54304
[7] H. Furstenberg,Strict ergodicity and transformation of the torus, Amer. J. Math.83 (1961), 573–601. · Zbl 0178.38404
[8] H. Furstenberg,The unique ergodicity of the horocycle flow, Recent Advances in Topological Dynamics, Springer-Verlag Lecture Notes in Math. 318, 95–114.
[9] M. Hirsch and C. Pugh,Stable manifolds and hyperbolic sets, Proc. Symp. Pure Math.14, Amer. Math. Soc., Providence, R. I., 1970, 133–163. · Zbl 0215.53001
[10] N. Kryloff and N. Bogoliuboff,La théorie générale de la mesure dans son application à l’étude des systèmes dynamiques non linéaires. Ann. of Math.38 (1937), 65–113. · Zbl 0016.08604
[11] B. Marcus,Reparametrizations of uniquely ergodic flows, to appear in J. Differential Equations. · Zbl 0295.28022
[12] S. Newhouse,On codimension one Anosov diffeomorphisms, Amer. J. Math.92 (1970), 761–770. · Zbl 0204.56901
[13] V. V. Nemytzkii and V. V. Stepanov,Qualitative Theory of Differential Equations, Princeton University Press, Princeton, 1960, Ch. V.2.
[14] D. Ruelle and D. Sullivan,Currents, Flows, and Diffeomorphisms, preprint.
[15] Ya. G. Sinai,Markov partitions and C-diffeomorphisms, Functional Anal. Appl.2 (1968), 64–89. · Zbl 0182.55003
[16] S. Smale,Differentiable dynamical systems, Bull. Amer. Math. Soc.73 (1967), 747–817. · Zbl 0202.55202
[17] P. Walters,Introductory Lectures on Ergodic Theory, lecture notes, University of Maryland. · Zbl 0239.28011
[18] H. Whitney,Regular families of curves, Ann. of Math.34 (1933), 269. · Zbl 0006.37101
[19] R. F. Williams,One dimensional non-wandering sets, Topology6 (1967), 473–487. · Zbl 0159.53702
[20] R. F. Williams,Classification of one dimensional attractors, Proc. Symp. Pure Math.14, Amer. Math. Soc., Providence, R. I., 1970, 341–361. · Zbl 0213.50401
[21] R. F. Williams, written communication.
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.