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On piecewise affine interval maps with countably many laps
1. | KM FSv ČVUT, Thákurova 7, 166 29 Praha 6, Czech Republic, Czech Republic |
References:
[1] |
J. Bobok and M. Soukenka, Irreducibility, infinite level sets and small entropy, to appear in Real Analysis Exchange, 36 (2011). |
[2] |
E. M. Coven and M. C. Hidalgo, On the topological entropy of transitive maps of the interval, Bull. Aust. Math. Soc., 44 (1991), 207-213. |
[3] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995. |
[4] |
M. Misiurewicz, Horseshoes for mappings of an interval, Bull. Acad. Pol. Sci., Sér. Sci. Math., 27 (1979), 167-169. |
[5] |
M. Misiurewicz and P. Raith, Strict inequalities for the entropy of transitive piecewise monotone maps, Discrete and Continuous Dynamical Systems, 13 (2005), 451-468.
doi: 10.3934/dcds.2005.13.451. |
[6] |
J. Milnor and W. Thurston, On iterated maps of the interval, in "Dynamical Systems" (College Park, MD, 1986-1987), Lecture Notes in Math., 1342, Springer, Berlin, (1988), 465-563. |
[7] |
W. Parry, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc., 122 (1966), 368-378.
doi: 10.1090/S0002-9947-1966-0197683-5. |
[8] |
P. Walters, "An Introduction to Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
show all references
References:
[1] |
J. Bobok and M. Soukenka, Irreducibility, infinite level sets and small entropy, to appear in Real Analysis Exchange, 36 (2011). |
[2] |
E. M. Coven and M. C. Hidalgo, On the topological entropy of transitive maps of the interval, Bull. Aust. Math. Soc., 44 (1991), 207-213. |
[3] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995. |
[4] |
M. Misiurewicz, Horseshoes for mappings of an interval, Bull. Acad. Pol. Sci., Sér. Sci. Math., 27 (1979), 167-169. |
[5] |
M. Misiurewicz and P. Raith, Strict inequalities for the entropy of transitive piecewise monotone maps, Discrete and Continuous Dynamical Systems, 13 (2005), 451-468.
doi: 10.3934/dcds.2005.13.451. |
[6] |
J. Milnor and W. Thurston, On iterated maps of the interval, in "Dynamical Systems" (College Park, MD, 1986-1987), Lecture Notes in Math., 1342, Springer, Berlin, (1988), 465-563. |
[7] |
W. Parry, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc., 122 (1966), 368-378.
doi: 10.1090/S0002-9947-1966-0197683-5. |
[8] |
P. Walters, "An Introduction to Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
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