The dynamics of piecewise monotonic maps under small perturbations

Peter Raith

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 24, Issue: 4, page 783-811
  • ISSN: 0391-173X

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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 24.4 (1997): 783-811. <http://eudml.org/doc/84279>.

@article{Raith1997,
author = {Raith, Peter},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {periodic point; structural decomposition; nonwandering set; maximal topologically transitive subsets},
language = {eng},
number = {4},
pages = {783-811},
publisher = {Scuola normale superiore},
title = {The dynamics of piecewise monotonic maps under small perturbations},
url = {http://eudml.org/doc/84279},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Raith, Peter
TI - The dynamics of piecewise monotonic maps under small perturbations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 24
IS - 4
SP - 783
EP - 811
LA - eng
KW - periodic point; structural decomposition; nonwandering set; maximal topologically transitive subsets
UR - http://eudml.org/doc/84279
ER -

References

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  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

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