Entropies et représentation markovienne des applications régulières de l'intervalle
Thèses d'Orsay, no. 405 (1995) , 190 p.
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     title = {Entropies et repr\'esentation markovienne des applications r\'eguli\`eres de l'intervalle},
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     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
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     url = {http://www.numdam.org/item/BJHTUP11_1995__0405__P0_0/}
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Buzzi, Jérôme. Entropies et représentation markovienne des applications régulières de l'intervalle. Thèses d'Orsay, no. 405 (1995), 190 p. http://numdam.org/item/BJHTUP11_1995__0405__P0_0/

[1] A.M. Blokh, Decomposition of dynamical systems on an interval, Russ. Math. Surv. 38 (1983), 133-134. | Zbl | DOI

[2] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414. | MR | Zbl | DOI

[3] R. Bowen, Entropy-expansive maps, Trans. Amer. Math. Soc. 164 (1972), 323-333. | MR | Zbl | DOI

[4] R. Bowen, Topological entropy for non-compact sets, Trans. Amer. Math. Soc. 184 (1973), 125-136. | MR | Zbl | DOI

[5] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, LNM 470, Springer, 1975. | MR | Zbl

[6] R. Bowen, Some systems with unique equilibrium state, Math. Sys. Th. 8 (1975), 193-202. | MR | Zbl | DOI

[7] M. Denker, Measures with maximal entropy, Journées ergodiques, LNM Springer. | Zbl | DOI

[8] M. Denker, C. Grillenberg, K. Sigmund, Ergodic theory on compact spaces, LNM 527, Springer-Verlag, 1976. | MR | Zbl

[9] B.A. Doubrovine, S.P. Novikov, A.T. Fomenko, Géométrie contemporaine, Editions Mir, Moscou, 1982.

[10] T.N.T. Goodman, Maximal measures for expansive homeomorphisms, J. London Math. Soc. 2 (1972), 439-444. | MR | Zbl | DOI

[11] M. Gromov, Entropy, homology and semi-algebraic geometry, Séminaire Bourbaki 663 (1985-1986). | MR | Zbl | Numdam

[12] J. Guckenheimer, Sensitive dependence on initial conditions for one dimensional maps, Comm. Math. Phys. 70 (1979), 133-160. | MR | Zbl | DOI

[13] B.M. Gurevič, Topological entropy of enumerable Markov chains, Soviet Math. Dokl. 10 (1969), 911-915. | Zbl

[14] B.M. Gurevič, Shift entropy and Markov measures in the path space of a denumerable graph, Soviet Math. Dokl. 11 (1970), 744-747. | Zbl

[15] F. Hofbauer, ?-shifts have unique maximal measure, Mh. Math. 85 (1978), 189-198. | MR | Zbl | DOI

[16] F. Hofbauer, On intrinsic ergodicity of piecewise monotonie transformations with positive entropy, Israel J. Math. I 34 (1979), 213-237 ; II 38 (1981), 107-115. | MR | Zbl | DOI

[17] F. Hofbauer, The structure of piecewise monotonic transformations, Ergod. Th. & Dynam. Sys. 1 (1981), 159-178. | MR | Zbl | DOI

[18] F. Hofbauer, Kneading invariants and Markov diagrams, Ergodic theory and related topics (Vitt) (H. Michels, ed.), 1982. | MR | Zbl

[19] F. Hofbauer, Piecewise invertible dynamical systems, Prob. Th. Rel. Fields 72 (1986), 359-386. | MR | Zbl | DOI

[20] F. Hofbauer, G. Keller, Quadratic maps without asymptotic measure, Comm. Math. Phys. 127 (1990), 319-337. | MR | Zbl | DOI

[21] L.B. Jonker, D.A. Rand, Bifurcations in one dimension, Invent. Math. I 62 (1981), 347-365 | Zbl

[21] L.B. Jonker, D.A. Rand, Bifurcations in one dimension, Invent. Math. II 63 (1981), 1-16. | MR | Zbl | DOI

[22] A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publ. Math. I.H.E.S. 51 (1980), 137-173. | MR | Zbl | Numdam | DOI

[23] G. Keller, Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems, Trans. Amer. Math. Soc 314 (1989), 433-497. | MR | Zbl | DOI

[24] G. Keller, Lifting measures to Markov extensions, Mh. Math. 108 (1989), 183-200. | MR | Zbl | DOI

[25] G. Keller, Exponents, attractors, and Hopf decomposition for interval maps, Ergod. Th. & Dynam. Sys. 10 (1990), 717-744. | MR | Zbl | DOI

[26] B. Kitchens, Countable Markov shifts (preprint IBM T.J. Watson Research Center).

[27] T. Krüger, S. Troubetzkoy, Symbolic dynamics for diffeomorphisms with no zero Lyapunoff exponents, Ergodic Theory and Dynamical Systems. Torun 1994, non-publié.

[28] F. Ledrappier, Some properties of absolutely continuous invariant measures of an interval, Ergod. Th. & Dynam. Sys. 1 (1981), 77-93. | MR | Zbl | DOI

[29] B. Marcus, S.E. Newhouse, Measures of maximal entropy for a class of skew-products, Lecture Notes in Math. 729, Springer. | MR | Zbl

[30] M. Misiurewicz, Diffeomorphisms without any measures of maximal entropy, Bull. Acad. Polon. Sci. Ser. Math. Astron. Phys. 21 (1973), 903-910. | MR | Zbl

[31] M. Misiurewicz, Topological conditional entropy, Studia Math. 55 (1976), 175-200. | MR | Zbl | DOI

[32] S.E. Newhouse, Volume growth and entropy, Ergod. Th. & Dynam. Sys. 8* (1988), 283-299. | MR | Zbl

[33] S.E. Newhouse, Continuity properties of the entropy, Ann. Math. 129 (1989), 215-237. | MR | Zbl | DOI

[34] S.E. Newhouse, On some results of Hofbauer on maps of the interval, Proceedings, Nagoya 1991. | MR

[35] S.E. Newhouse, L.-S. Young, Dynamics of certain skew products, Geometric Dynamics, Proc. Rio de Janeiro 1981. LNM 1007, Springer, 1983. | MR | Zbl | DOI

[36] W. Parry, Intrinsic Markov chains, Trans. Amer. Math. Soc. 112 (1964), 55-66. | MR | Zbl | DOI

[37] K. Petersen, Ergodic theory, Cambridge University Press, 1983. | MR | Zbl | DOI

[38] K. Petersen, Chains, entropy, coding, Ergod. Th. & Dynam. Sys. 6 (1986), 415-448. | MR | Zbl | DOI

[39] D.J. Rudolph, Fundamentals of measurable dynamics, Clarendon Press, Oxford, 1990. | MR | Zbl

[40] D. Ruelle, An inequality for the entropy of differentiable maps, Bol. Soc. Bras. Mat. 9 (1978), 83-87. | MR | Zbl | DOI

[41] D. Ruelle, Thermodynamic formalism, Addison-Wesley, 1979. | MR

[42] I.A. Salama, Topological entropy and classification of countable chains, Ph.D. thesis, University of North Carolina, Chapel Hill, 1984. | MR

[43] E. Seneta, Non-negative matrices and Markov chains, Springer, 1981. | MR | Zbl | DOI

[44] Y. Takahashi, Osaka J. Math. 10 (1973), 175-184. | MR | Zbl

[45] S. Van Strien, W. De Melo, One-dimensional dynamics, Springer, 1993. | MR | Zbl

[46] D. Vere-Jones, Geometric ergodicity in denumerable Markov chains, Quarterly J. Math. 13 (1962), 7-28. | MR | Zbl | DOI

[47] D. Vere-Jones, Ergodic properties of nonnegative matrices I, Pacific J. Math. 22 (1967), 361-386. | MR | Zbl | DOI

[48] P. Walters, An introduction to ergodic theory, Springer, 1981. | Zbl | MR

[49] B. Weiss, Intrinsically ergodic systems, Bull. Amer. Math. Soc. 76 (1970), 1266-1269. | MR | Zbl | DOI

[50] B. Weiss, Subshifts of finite type and sofic systems, Monatsh. Math. 77 (1973), 462-474. | MR | Zbl | DOI

[51] Y. Yomdin, Volume growth and entropy, Israel J. Math. 57 (1987), 285-300. | MR | Zbl | DOI

[52] Y. Yomdin, Ck-resolution of semi-algebraic mappings, Israel J. Math. 57 (1987), 301-318. | MR | Zbl

[53] F. Hofbauer, Generic properties of invariant measures for continuous piecewise monotonic transformations, Monat. Math. 106 (1988), 301-312. | MR | Zbl | DOI

[54] F. Hofbauer, P. Raith, Topologically transitive subsets of piecewise monotonic maps, which contains no periodic points, Monat. Math. 107 (1989), 217-239. | MR | Zbl | DOI