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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fractal properties of invariant subsets for piecewise monotonic maps on the interval


Authors: Franz Hofbauer and Mariusz Urbański
Journal: Trans. Amer. Math. Soc. 343 (1994), 659-673
MSC: Primary 58F11; Secondary 28D05, 58F13
MathSciNet review: 1232188
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Abstract: Let T be a piecewise monotonic transformation on [0, 1] and let A be a T-invariant subset, which has positive topological entropy and satisfies the Darboux property. A general existence theorem for conformal measures on A is proved. This is then used to show equality of the dynamical dimension of A and the minimal zero of a certain pressure function.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1232188-9
Article copyright: © Copyright 1994 American Mathematical Society