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Fractal dimensions and homeomorphic conjugacies |
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| Authors: | A. Arneodo M. Holschneider |
| Affiliation: | (1) Center for Nonlinear Dynamics, Physics Department, University of Texas, 78712 Austin, Texas;(2) Present address: Laboratoire de Physique Théorique, Université de Nice, 06034 Nice, France;(3) Centre de Physique Théorique, CNRS-Luminy, Case 907, 13288 Marseille, France;(4) Present address: Mathematisches Institut, Ruhr Universitat, 8630 Bochum 1, Germany |
| Abstract: | We investigate the behavior of the spectrum of singularities associated with the invariant measure of some dynamical systems under nonsmooth coordinate changes. When the homeomorphic conjugacy is not Lipschitz continuous, we discuss how its singularities can affect the whole set of generalized fractal dimensions. We give applications to homeomorphisms that conjugate critical circle maps with irrational (golden mean) winding numbers. We present numerical studies corroborating the theoretical predictions. |
| Keywords: | Fractal dimensions spectrum of singularities invariant measures homeomorphic conjugacies critical circle maps |
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