Abstract
In this paper a piecewise monotonic mapT:X→ℝ, whereX is a finite union of intervals, is considered. DefineR(T)= $$\mathop \cap \limits_{n = 0}^\infty \overline {T^{ - n} X} $$ . The influence of small perturbations ofT on the Hausdorff dimension HD(R(T)) ofR(T) is investigated. It is shown, that HD(R(T)) is lower semi-continuous, and an upper bound of the jumps up is given. Furthermore a similar result is shown for the topological pressure.
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