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Number of equilibrium states of piecewise monotonic maps of the interval

Author: Jérôme Buzzi
Journal: Proc. Amer. Math. Soc. 123 (1995), 2901-2907
MSC: Primary 58F11; Secondary 28D20, 54H20, 58F03
Erratum: Proc. Amer. Math. Soc. 125 (1997), 3131.
MathSciNet review: 1277099
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Abstract: We prove a bound of the form suggested by S. Newhouse for the number of measures with maximal entropy for a piecewise monotonic map with N monotonicity intervals: $ 4(N - 1)$. More generally we consider a potential $ \phi $ of bounded distortion. If $ \sup \phi < P(f,\phi )$, we give an explicit bound in terms of N and of the pressure.

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Article copyright: © Copyright 1995 American Mathematical Society

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