Abstract
AbstractThe continuity of Hausdorff dimension of closed invariant subsetsKof aC2-expanding mappinggof the circle is investigated. Ifg/Ksatisfies the specification property then the equilibrium states of Hölder continuous functions are studied. It is proved that iffis a piecewise monotone continuous mapping of a compact interval and φ a continuous function withP(f,φ)> sup(φ), then the pressureP(f,φ) is attained on one-dimensional ‘Smale's horseshoes’, and some results of Misiurewicz and Szlenk [M−Sz] are extended to the case of pressure.
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