Fractal properties of invariant subsets for piecewise monotonic maps on the interval
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- by Franz Hofbauer and Mariusz Urbański
- Trans. Amer. Math. Soc. 343 (1994), 659-673
- DOI: https://doi.org/10.1090/S0002-9947-1994-1232188-9
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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.References
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Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 343 (1994), 659-673
- MSC: Primary 58F11; Secondary 28D05, 58F13
- DOI: https://doi.org/10.1090/S0002-9947-1994-1232188-9
- MathSciNet review: 1232188