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Dimension-like characteristics of invariant sets in dynamical systems. (English) Zbl 1031.37024
Maass, Alejandro (ed.) et al., Dynamics and randomness. Lectures given at the conference, Universidad de Chile, Santiago, Chile, December 11-15, 2000. Dordrecht: Kluwer Academic Publishers. Nonlinear Phenom. Complex Syst. 7, 1-30 (2002).
The authors give a survey of the theory of dimension-like characteristics of invariant sets. The following topics are included: Hausdorff dimension, topological pressure, generalized Carathéodory construction and spectra of dimension for Poincaré recurrences, local dimensions and dimensions of measures for Poincaré recurrences. Some instructive and nontrivial examples (such as sticky sets and conformal repellers) are discussed in detail.
For the entire collection see [Zbl 1019.00010].

##### MSC:
 37C45 Dimension theory of smooth dynamical systems 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems