Measures of maximal entropy

Subject Areas : Abstract harmonic analysis

M. Amini ¹

1 - Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran

Received: 2019-02-28 Accepted : 2019-03-17 Published : 2019-12-01

Keywords:

References:

[1] J. Aaronson, An Introduction to Infinite Ergodic Theory, Mathematical Surveys and Monographs 50, American Mathematical Society, Providence, 1997.

[2] M. Amini, Invariant measures on non compact dynamics, preprint.

[3] K. R. Berg, Convolution of invariant measures, maximal entropy, Math. Syst. Theory. 3 (1969), 146-151.

[4] L. W. Goodwyn, Comparing topological entropy with measure-theoretic entropy, Amer. J. Math. 94 (1972), 366-388.

[5] B. M. Gurevic, Topological entropy of denumerable Markov chains, Soviet Math. Dokl. 10 (4) (1969), 911-915.

[6] N. Krylov, N. Bogolioubov, La th´eorie g´en´erale de la mesure dans son application ´al’´etude des syst´emes
dynamiques de la m´ ecanique non lin´ eaire, Ann. Math. 38 (1937), 65-113.

[7] V. V. Nemycki˘i, V. V. Stepanov, Qualitative Theory of Differential Equations, 2nd Ed., Moscow, 1949.

[8] J. C. Oxtoby, S. M. Ulam, On the existence of a measure invariant under a transformation, Annals Math. 40 (1939), 560-566.

[9] K. Sakai, Various shadowing properties for positively expansive maps, Topol. Appl. 131 (2003), 15-31.

[10] M. Viana, K. Oliveira, Foundations of Ergodic Theory, Cambridge Studies in Advanced Mathematics 151, Cambridge University Press, 2016.

[11] P. Walters, Ergodic theory-Introductory lectures, Lecture Notes in Math. 458, Springer-Verlag, New York, 1975.

[12] P. Walters, Invariant measures and equilibrium states for some mappings which expand distances, Trans. Amer. Math. Soc. 236 (1978), 121-153.

[13] P. Walters, Some transformations having a unique measure with maximal entropy, Proc. London Math. Soc. (3) 28 (1974), 500-516.

[14] B. Weiss, Intrinsically ergodic systems, Bull. Amer. Math. Soc. 76 (1970), 1266-1269.