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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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