Bowen, R. Entropy for group endomorphisms and homogeneous spaces. (English) Zbl 0212.29201 Trans. Am. Math. Soc. 153, 401-414 (1971). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 20 ReviewsCited in 495 Documents MSC: 54C70 Entropy in general topology 54H20 Topological dynamics (MSC2010) × Cite Format Result Cite Review PDF Full Text: DOI 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] Rufus Bowen, Periodic points and measures for Axiom \? diffeomorphisms, Trans. Amer. Math. Soc. 154 (1971), 377 – 397. · Zbl 0212.29103 [3] L. Wayne Goodwyn, Topological entropy bounds measure-theoretic entropy, Proc. Amer. Math. Soc. 23 (1969), 679 – 688. · Zbl 0186.09804 [4] -, The product theorem for topological entropy (to appear). [5] James R. Munkres, Elementary differential topology, Lectures given at Massachusetts Institute of Technology, Fall, vol. 1961, Princeton University Press, Princeton, N.J., 1963. · Zbl 0107.17201 [6] William Parry, Entropy and generators in ergodic theory, W. A. Benjamin, Inc., New York-Amsterdam, 1969. · Zbl 0175.34001 [7] Ja. Sinaĭ, On the concept of entropy for a dynamic system, Dokl. Akad. Nauk SSSR 124 (1959), 768 – 771 (Russian). Ja. Sinaĭ, Flows with finite entropy, Dokl. Akad. Nauk SSSR 125 (1959), 1200 – 1202 (Russian). [8] V. A. Rohlin, Exact endomorphisms of a Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 499 – 530 (Russian). [9] A. L. Genis, Metric properties of the endomorphisms of an \?-dimensional torus, Dokl. Akad. Nauk SSSR 138 (1961), 991 – 993 (Russian). · Zbl 0206.42701 [10] D. Z. Arov, Calculation of entropy for a class of group endomorphisms, Zap. Meh.-Mat. Fak. Har\(^{\prime}\)kov. Gos. Univ. i Har\(^{\prime}\)kov. Mat. Obšč. (4) 30 (1964), 48 – 69 (Russian). [11] K. Krzyżewski and W. Szlenk, On invariant measures for expanding differentiable mappings, Studia Math. 33 (1969), 83 – 92. · Zbl 0176.00901 [12] K. Berg, Thesis, Minnesota. [13] -, Convolution of invariant measures, maximum entropy (to appear). [14] Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. · Zbl 0068.01904 [15] Harvey B. Keynes, Lifting of topological entropy, Proc. Amer. Math. Soc. 24 (1970), 440 – 445. · Zbl 0188.28203 [16] Claude Chevalley, Theory of Lie groups. I, Princeton University Press, Princeton, N. J., 1946 1957. · Zbl 0063.00842 [17] D. V. Anosov and Ja. G. Sinaĭ, Certain smooth ergodic systems, Uspehi Mat. Nauk 22 (1967), no. 5 (137), 107 – 172 (Russian). · Zbl 0177.42002 [18] Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Company, Inc., Toronto-New York-London, 1953. · Zbl 0052.11701 [19] William Parry, Ergodic properties of affine transformations and flows on nilmanifolds., Amer. J. Math. 91 (1969), 757 – 771. · Zbl 0183.51503 · doi:10.2307/2373350 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.