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Formulas for the topological entropy of multimodal maps based on min-max symbols
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Semiconjugacy to a map of a constant slope
1. | Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08913 Cerdanyola del Vallès, Barcelona |
2. | Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202 |
References:
[1] |
Ll. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One,, Second Edition, (2000).
doi: 10.1142/4205. |
[2] |
A. M. Blokh, Sensitive mappings of an interval,, Uspekhi Mat. Nauk., 37 (1982), 189.
|
[3] |
M. Denker, G. Keller and M. Urbañski, On the uniqueness of equilibrium states for piecewise monotone mappings,, Studia Math., 97 (1990), 27.
|
[4] |
F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II,, Israel J. Math., 38 (1981), 107.
doi: 10.1007/BF02761854. |
[5] |
T.-Y. Li and J. A. Yorke, Ergodic transformations from an interval into itself,, Trans. Amer. Math. Soc., 235 (1978), 183.
doi: 10.1090/S0002-9947-1978-0457679-0. |
[6] |
J. Llibre and M. Misiurewicz, Horseshoes, entropy and periods for graph maps,, Topology, 32 (1993), 649.
doi: 10.1016/0040-9383(93)90014-M. |
[7] |
J. Milnor and W. Thurston, On iterated maps of the interval,, in Dynamical Systems (College Park, (1342), 1986.
doi: 10.1007/BFb0082847. |
[8] |
M. Misiurewicz, Absolutely continuous measures for certain maps of an interval,, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 17.
|
[9] |
M. Misiurewicz, Possible jumps of entropy for interval maps,, Qualit. Th. Dyn. Sys., 2 (2001), 289.
doi: 10.1007/BF02969344. |
[10] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings,, Studia Math., 67 (1980), 45.
|
[11] |
M. Misiurewicz and K. Ziemian, Horseshoes and entropy for piecewise continuous piecewise monotone maps,, in From Phase Transitions to Chaos, (1992), 489.
|
[12] |
W. Parry, Symbolic dynamics and transformations of the unit interval,, Trans. Amer. Math. Soc., 122 (1966), 368.
doi: 10.1090/S0002-9947-1966-0197683-5. |
[13] |
P. Raith, Hausdorff dimension for piecewise monotonic maps,, Studia Math., 94 (1989), 17.
|
[14] |
P. Walters, An Introduction to Ergodic Theory,, Graduate Texts in Mathematics, (1982).
|
show all references
References:
[1] |
Ll. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One,, Second Edition, (2000).
doi: 10.1142/4205. |
[2] |
A. M. Blokh, Sensitive mappings of an interval,, Uspekhi Mat. Nauk., 37 (1982), 189.
|
[3] |
M. Denker, G. Keller and M. Urbañski, On the uniqueness of equilibrium states for piecewise monotone mappings,, Studia Math., 97 (1990), 27.
|
[4] |
F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II,, Israel J. Math., 38 (1981), 107.
doi: 10.1007/BF02761854. |
[5] |
T.-Y. Li and J. A. Yorke, Ergodic transformations from an interval into itself,, Trans. Amer. Math. Soc., 235 (1978), 183.
doi: 10.1090/S0002-9947-1978-0457679-0. |
[6] |
J. Llibre and M. Misiurewicz, Horseshoes, entropy and periods for graph maps,, Topology, 32 (1993), 649.
doi: 10.1016/0040-9383(93)90014-M. |
[7] |
J. Milnor and W. Thurston, On iterated maps of the interval,, in Dynamical Systems (College Park, (1342), 1986.
doi: 10.1007/BFb0082847. |
[8] |
M. Misiurewicz, Absolutely continuous measures for certain maps of an interval,, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 17.
|
[9] |
M. Misiurewicz, Possible jumps of entropy for interval maps,, Qualit. Th. Dyn. Sys., 2 (2001), 289.
doi: 10.1007/BF02969344. |
[10] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings,, Studia Math., 67 (1980), 45.
|
[11] |
M. Misiurewicz and K. Ziemian, Horseshoes and entropy for piecewise continuous piecewise monotone maps,, in From Phase Transitions to Chaos, (1992), 489.
|
[12] |
W. Parry, Symbolic dynamics and transformations of the unit interval,, Trans. Amer. Math. Soc., 122 (1966), 368.
doi: 10.1090/S0002-9947-1966-0197683-5. |
[13] |
P. Raith, Hausdorff dimension for piecewise monotonic maps,, Studia Math., 94 (1989), 17.
|
[14] |
P. Walters, An Introduction to Ergodic Theory,, Graduate Texts in Mathematics, (1982).
|
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