The dynamics of piecewise monotonic maps under small perturbations

 Access to full text

 Full (PDF)

1. [ 1 ] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics470, Springer, Berlin, 1975. Zbl0308.28010MR442989
2. [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. Zbl0422.28015MR570882
3. [3] F. Hofbauer, The structure of piecewise monotonic transformations, Ergodic Theory Dynamical Systems1 (1981), 159-178. Zbl0474.28007MR661817
4. [4] F. Hofbauer, Piecewise invertible dynamical systems, Probab. Theory Related Fields72 (1986), 359-386. Zbl0578.60069MR843500
5. [5] F. Hofbauer - P. Raith, Topologically transitive subsets of piecewise monotonic maps, which contain no periodic points, Monatsh. Math.107 (1989), 217-239. Zbl0676.54049MR1008681
6. [6] M. Misiurewicz, Jumps of entropy in one dimension, Fund. Math.132 (1989), 215-226. Zbl0694.54019MR1002409
7. [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. Zbl1026.37504MR1184170
8. [8] M. Misiurewicz - W. Szlenk, Entropy of piecewise monotone mappings, Studia Math. 67 (1980), 45-63. Zbl0445.54007MR579440
9. [9] J.D. Newburgh, The variation of spectra, Duke Math. J.18 (1951), 165-176. Zbl0042.12302MR51441
10. [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 Mathematics21, Birkhäuser, Boston, 1982, 1-73. Zbl0506.54035MR670074
11. [11] P. Raith, Hausdorff dimension for piecewise monotonic maps, Studia Math. 94 (1989), 17-33. Zbl0687.58013MR1008236
12. [12] P. Raith, Continuity of the Hausdorff dimension for piecewise monotonic maps, Israel J. Math.80 (1992), 97-133. Zbl0768.28010MR1248929
13. [13] P. Raith, The behaviour of the nonwandering set of a piecewise monotonic interval map under small perturbations, Math. Bohem.122 (1997), 37-55. Zbl0896.58027MR1446398
14. [14] P. Raith, Stability of the maximal measure for piecewise monotonic interval maps, Ergodic Theory Dynam. Systems (to appear), Preprint, Wien, 1995. Zbl0898.58015MR1488327
15. [15] M. Urba, Invariant subsets of expanding mappings of the circle, Ergodic Theory Dynamical Systems7 (1987), 627-645. Zbl0653.58031MR922369
16. [16] P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics 79, Springer, New York, 1982. Zbl0475.28009MR648108

1. Peter Raith, On the continuity of the pressure for monotonic mod one transformations