Peter Raith

Continuity of the hausdorff dimension for piecewise monotonic maps

AbstractIn this paper a piecewise monotonic mapT:X→ℝ, whereX is a finite union of intervals, is considered. DefineR(T)=

Hausdorff dimension for some hyperbolic attractors with overlaps and without finite Markov partition

\mathop \cap \limits_{n = 0}^\infty \overline {T^{ - n} X}

Stability of the topological pressure for piecewise monotonic maps underC 1-perturbations

. 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.

The space of ω-limit sets of piecewise continuous maps of the interval

If one splits the nonwandering set of a piecewise monotonic map into maximal subsets, which are topologically transitive, one gets two kinds of subsets. The first kind of these subsets has periodic orbits dense, the second kind contains no periodic orbits. In this paper it is shown, that there are only finitely many subsets of the second kind, each of which is minimal and has only finitely many ergodic invariant Borel probability measures.

Stability of the ω-limit set for unimodal transformations

In this paper some families of skew product self-maps

The Hausdorff dimension of an ergodic invariant measure for a piecewise monotonic map of the interval

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Hausdorff dimension for piecewise monotonic maps

on the square are considered. The main example is a family forming a two-dimensional analogue of the tent map family. According to the assumptions made in this paper these maps are almost injective. This means that the points of the attractor having more than one inverse image form a set of measure zero for all interesting measures. It may be that

Intermingled basins in a two species system

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