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Invariant subsets of expanding mappings of the circle

Published online by Cambridge University Press:  19 September 2008

Mariusz Urbański
Mariusz Urbański
Affiliation:
Institute of Mathematics, N. Copernicus University in Toruń, ul. Chopina 12/18, 87–100 Toruń, Poland
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Abstract

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The continuity of Hausdorff dimension of closed invariant subsets K of a C2-expanding mapping g of the circle is investigated. If g/K satisfies the specification property then the equilibrium states of Hölder continuous functions are studied. It is proved that if f is a piecewise monotone continuous mapping of a compact interval and φ a continuous function with P(f,φ)> sup(φ), then the pressure P(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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 4 , December 1987 , pp. 627 - 645
Copyright
Copyright © Cambridge University Press 1987

References

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