On a general concept of multifractality: Multifractal spectra for dimensions, entropies, and Lyapunov exponents. Multifractal rigidity
Copyright policy )On a general concept of multifractality: Multifractal spectra for dimensions, entropies, and Lyapunov exponents. Multifractal rigidity
We introduce the mathematical concept of multifractality and describe various multifractal spectra for dynamical systems, including spectra for dimensions and spectra for entropies. We support the study by providing some physical motivation and describing several nontrivial examples. Among them are subshifts of finite type and one-dimensional Markov maps. An essential part of the article is devoted to the concept of multifractal rigidity. In particular, we use the multifractal spectra to obtain a “physical’’ classification of dynamical systems. For a class of Markov maps, we show that, if the multifractal spectra for dimensions of two maps coincide, then the maps are differentiably equivalent.
- Pennsylvania State University United States
- Leibniz Association Germany
- Weierstrass Institute Germany
- Weierstrass Institute for Applied Analysis and Stochastics Germany
- Instituto Superior de Espinho Portugal
ddc:510, Ergodic theorems, spectral theory, Markov operators, Conformal repeller -- Gibbs measure -- local entropy -- Lyapunov exponents -- multifractal analysis -- multifractal rigidity -- pointwise dimension, one-dimensional Markov maps, article, Ergodicity, mixing, rates of mixing, multifractionality, Lyapunov exponents, pointwise dimension, Gibbs measure, local entropy, 530, multifractal rigidity, Strange attractors, chaotic dynamics of systems with hyperbolic behavior, multifractal spectra, 510, spectra for entropies, Conformal repeller, Dynamical systems with hyperbolic behavior, multifractal analysis
ddc:510, Ergodic theorems, spectral theory, Markov operators, Conformal repeller -- Gibbs measure -- local entropy -- Lyapunov exponents -- multifractal analysis -- multifractal rigidity -- pointwise dimension, one-dimensional Markov maps, article, Ergodicity, mixing, rates of mixing, multifractionality, Lyapunov exponents, pointwise dimension, Gibbs measure, local entropy, 530, multifractal rigidity, Strange attractors, chaotic dynamics of systems with hyperbolic behavior, multifractal spectra, 510, spectra for entropies, Conformal repeller, Dynamical systems with hyperbolic behavior, multifractal analysis
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