The dynamics of piecewise monotonic maps under small perturbations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 24 (1997) no. 4, pp. 783-811.
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Raith, Peter. The dynamics of piecewise monotonic maps under small perturbations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 24 (1997) no. 4, pp. 783-811. http://www.numdam.org/item/ASNSP_1997_4_24_4_783_0/

[ 1 ] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics 470, Springer, Berlin, 1975. | MR | Zbl

[2] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy, Israel J. Math. 34 (1979), 213-237; Part 2 Israel J. Math. 38 (1981), 107-115. | MR | Zbl

[3] F. Hofbauer, The structure of piecewise monotonic transformations, Ergodic Theory Dynamical Systems 1 (1981), 159-178. | MR | Zbl

[4] F. Hofbauer, Piecewise invertible dynamical systems, Probab. Theory Related Fields 72 (1986), 359-386. | MR | Zbl

[5] F. Hofbauer - P. Raith, Topologically transitive subsets of piecewise monotonic maps, which contain no periodic points, Monatsh. Math. 107 (1989), 217-239. | EuDML | MR | Zbl

[6] M. Misiurewicz, Jumps of entropy in one dimension, Fund. Math. 132 (1989), 215-226. | EuDML | MR | Zbl

[7] M. Misiurewicz - S.V. Shlyachkov, Entropy of piecewise continuous interval maps, European Conference on Iteration Theory (ECIT 89), Batschuns, 1989 (Ch. Mira, N. Netzer, C. Simó, Gy. Targoński, eds.), World Scientific, Singapore,1991, 239-245. | MR | Zbl

[8] M. Misiurewicz - W. Szlenk, Entropy of piecewise monotone mappings, Studia Math. 67 (1980), 45-63. | EuDML | MR | Zbl

[9] J.D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176. | MR | Zbl

[10] Z. Nitecki, Topological dynamics on the interval, Ergodic Theory and Dynamical Systems, Vol. 2, Proceedings of the Special Year at the University of Maryland, 1979/1980 (A. Katok, ed.), Progress in Mathematics 21, Birkhäuser, Boston, 1982, 1-73. | MR | Zbl

[11] P. Raith, Hausdorff dimension for piecewise monotonic maps, Studia Math. 94 (1989), 17-33. | MR | Zbl

[12] P. Raith, Continuity of the Hausdorff dimension for piecewise monotonic maps, Israel J. Math. 80 (1992), 97-133. | MR | Zbl

[13] P. Raith, The behaviour of the nonwandering set of a piecewise monotonic interval map under small perturbations, Math. Bohem. 122 (1997), 37-55. | MR | Zbl

[14] P. Raith, Stability of the maximal measure for piecewise monotonic interval maps, Ergodic Theory Dynam. Systems (to appear), Preprint, Wien, 1995. | MR | Zbl

[15] M. Urba, Invariant subsets of expanding mappings of the circle, Ergodic Theory Dynamical Systems 7 (1987), 627-645. | MR | Zbl

[16] P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics 79, Springer, New York, 1982. | MR | Zbl