Number of equilibrium states of piecewise monotonic maps of the interval

Buzzi, Jérôme

doi:10.1090/S0002-9939-1995-1277099-4

Number of equilibrium states of piecewise monotonic maps of the interval
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by Jérôme Buzzi PDF

Proc. Amer. Math. Soc. 123 (1995), 2901-2907 Request permission

Erratum: Proc. Amer. Math. Soc. 125 (1997), 3131-3131.

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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