On Topological Entropy of Semigroups of Commuting Transformations

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1. [1] Adler R.L. , Konheim A.G., Mc.Andrew M.H. : Topological entropy. Trans. AMS114 (1965) 309-319 Zbl0127.13102MR175106
2. [2] Bowen R. : Topological entropy and Axiom A. Proc. Symp. Pure Math. Vol. 14 (1970)23-41 Zbl0207.54402MR262459
3. [3] Bowen R. : Entropy for group endomorphisms and homogeneous spaces. Trans. AMS153 (1971) 401-414 Zbl0212.29201MR274707
4. [4] Bowen R. : Entropy-expansive maps. Trans. AMS164 (1972) 323-331 Zbl0229.28011MR285689
5. [5] Conze J.P. : Entropie d'un groupe abelien de transformations. Z. Wahrscheinlichkeitstheorie verw. Geb.25 (1972) 11-30 Zbl0261.28015MR335754
6. [6] Denker M., Eberlein E. : Ergodic flows are strictly ergodic. Advances in Mathematics13 (1974) 437-473 Zbl0283.28012MR352403
7. [7] Eberlein E. : Einbettung von Strömungen in Funktionenräume durch Erzeuger vom endlichen Typ. Z. Wahrscheinlichkeitstheorie verw. Geb.27 (1973) 277-291 Zbl0268.28011MR364600
8. [8] Föllmer H. : On entropy and information gain in random fields. Z. Wahrscheinlichkeitstheorie verw. Geb.26 (1973) 207-217 Zbl0258.60029MR348829
9. [9] Goodwyn L.W. : The product theorem for topological entropy. Trans. AMS158 (1971) 445-452 Zbl0219.54036MR283782
10. [10] Goodwyn L.W. : Topological entropy bounds measure-theoretic entropy. Proc. AMS23 (1969) 679-688 Zbl0186.09804MR247030
11. [11] Goodwyn L.W. : Comparing topological entropy with measuretheoretic entropy. American Journal of Math.54 (1972) 366-388 Zbl0249.54021MR310191
12. [12] Jacobs K. : Lipschitz functions and the prevalence of strict ergodicity for continuous-time flows. Lecture Notes in Mathematics160. Springer-Verlag87-124 Zbl0201.38302MR274709
13. [13] Katznelson Y., Weiss B. : Commuting measure-preserving transformations. Israel J . Math.12 (1972) 161-173 Zbl0239.28014MR316680
14. [14] Keynes H., Robertson J. : Generators for topological entropy and expansiveness, Math. Syst. Theory3 (1969) 51-59 Zbl0176.20603MR247031
15. [15] Kolmogorov A.N., Tikhomirov V.M. : ε-entropy and ε-capacity of sets in funtional spaces. AMS Translations17 (1961) 277-364 Zbl0133.06703MR124720
16. [16] Krengel U. : K-flows are forward deterministic, backward completely non-deterministic stationary point processes. J. Math. Anal. Appl.35 (1971) 611-620 Zbl0215.26105MR287607
17. [17] Lind D.A. : Locally compact measure preserving flows. Advances in Mathematics15 (1975) 175-193 Zbl0293.28012MR382595
18. [18] Pickel. B.S., Stepin A. M. : On the entropy equidistribution property of commutative groups of metric automorphisms. Soviet. Math. Dokl.12 (1971) 938-942 Zbl0232.28017
19. [19] Rokhlin V.A. : Lectures on the entropy theory of measurepreserving transformations. Russ. Math. Surveys22 (1967) No. 51-52 Zbl0174.45501
20. [20] Thouvenot J.P. : Convergence en moyenne de l’information pour l’action de $Z^2$ . Z. Wahrscheinlichkeitstheorie verw. Geb.24 (1972) 135-137 Zbl0266.60037MR321612
21. [21] Elsanousi S.A. : A variational principle for the pressure of a continuous $Z^2$-action on a compact metric space. (to appear) Zbl0388.28021
22. [22] Goodman T.N.T. : Topological sequence entropy. Proc London Math Soc. (3) 29 (1974) 331-350 Zbl0293.54043MR356009
23. [23] Kushnirenko A.G. : On metric invariants of entropy type. Russ. Math. Surveys22 (1967) No. 553-61 Zbl0169.46101MR217257
24. [24] Misiurewicz M. : $A_N$ short proof of the variational principle for a $Z_{+}^N$-action on a compact space. (these Proceedings) Zbl0351.54036MR430213
25. [25] Newton D. : On sequence entropy I/II. Math. Systems Theory4 (1970) 119-128 Zbl0189.05704MR274714
26. [26] Newton D., Krug E. : On sequence entropy of automorphisms of a Lebesgue space. Z. Wahrscheinlichkeitstheorie verw. Geb.24 (1972) 211-214 Zbl0237.28009MR322136
27. [27] Ruelle D. : Statistical mechanics on a compact set with $Z^{\nu }$-action satisfying expansiveness and specification. Trans. AMS185 (1973) 237-251 Zbl0278.28012MR417391
28. [28] Walters P. : A variational principle for the pressure of continuous transformations. (to appear) Zbl0318.28007MR390180