## Topological entropy for noncompact sets.(English)Zbl 0274.54030

### MSC:

 54H20 Topological dynamics (MSC2010) 28D05 Measure-preserving transformations
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### References:

 [1] R. L. Adler, A. G. Konheim, and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309 – 319. · Zbl 0127.13102 [2] Roy L. Adler and Benjamin Weiss, Similarity of automorphisms of the torus, Memoirs of the American Mathematical Society, No. 98, American Mathematical Society, Providence, R.I., 1970. · Zbl 0195.06104 [3] Patrick Billingsley, Hausdorff dimension in probability theory, Illinois J. Math. 4 (1960), 187 – 209. · Zbl 0098.10602 [4] Patrick Billingsley, Ergodic theory and information, John Wiley & Sons, Inc., New York-London-Sydney, 1965. · Zbl 0184.43301 [5] Rufus Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401 – 414. · Zbl 0212.29201 [6] Rufus Bowen, Markov partitions for Axiom \? diffeomorphisms, Amer. J. Math. 92 (1970), 725 – 747. · Zbl 0208.25901 [7] C. M. Colebrook, The Hausdorff dimension of certain sets of nonnormal numbers, Michigan Math. J. 17 (1970), 103 – 116. · Zbl 0194.35802 [8] E. I. Dinaburg, A correlation between topological entropy and metric entropy, Dokl. Akad. Nauk SSSR 190 (1970), 19 – 22 (Russian). · Zbl 0196.26401 [9] H. G. Eggleston, The fractional dimension of a set defined by decimal properties, Quart. J. Math., Oxford Ser. 20 (1949), 31 – 36. · Zbl 0031.20801 [10] Harry Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967), 1 – 49. · Zbl 0146.28502 [11] Donald Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5 (1970), 339 – 348 (1970). , https://doi.org/10.1016/0001-8708(70)90008-3 Donald Ornstein, Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math. 5 (1970), 349 – 364 (1970). , https://doi.org/10.1016/0001-8708(70)90009-5 N. A. Friedman and D. S. Ornstein, On isomorphism of weak Bernoulli transformations, Advances in Math. 5 (1970), 365 – 394 (1970). · Zbl 0203.05801 [12] T. N. T. Goodman, Relating topological entropy and measure entropy, Bull. London Math. Soc. 3 (1971), 176 – 180. · Zbl 0219.54037 [13] L. Wayne Goodwyn, Topological entropy bounds measure-theoretic entropy, Proc. Amer. Math. Soc. 23 (1969), 679 – 688. · Zbl 0186.09804 [14] William Parry, Entropy and generators in ergodic theory, W. A. Benjamin, Inc., New York-Amsterdam, 1969. · Zbl 0175.34001 [15] D. Ruelle, Statistical mechanics on a compact set with $${Z^\nu }$$ action satisfying expansiveness and specification (preprint). · Zbl 0255.28015 [16] У-диффеоморпхисмс, Функционал. Анал. и Прилоžен 2 (1968), но. 1, 64 – 89 (Руссиан). [17] B. Weiss, Intrinsically ergodic systems, Bull. Amer. Math. Soc. 76 (1970), 1266 – 1269. · Zbl 0218.28011 [18] K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. · Zbl 0153.19101 [19] Robert Ash, Information theory, Interscience Tracts in Pure and Applied Mathematics, No. 19, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1965. · Zbl 0141.34904 [20] Karl Sigmund, On dynamical systems with the specification property, Trans. Amer. Math. Soc. 190 (1974), 285 – 299. · Zbl 0286.28010 [21] Benjamin Weiss, The isomorphism problem in ergodic theory, Bull. Amer. Math. Soc. 78 (1972), 668 – 684. · Zbl 0255.28014
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