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Multifractal dimensions for invariant subsets of piecewise monotonic interval maps. (English) Zbl 1051.37011
Multifractal dimensions of invariant sets of piecewise monotonic interval maps are studied and formulas for multifractal dimensions of invariant sets and ergodic invariant measures are derived. Previous results in this direction are obtained assuming the existence of a Markov partition which does not hold true, in general, in the situation considered in this paper.

MSC:
37C45 Dimension theory of smooth dynamical systems
28A80 Fractals
37E05 Dynamical systems involving maps of the interval
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