Global multifractal relation between topological entropies and fractal dimensions |
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| Institution: | 1. Department of Geosciences, University of Arizona, Tucson, AZ 85721, USA;2. Institut de Paléoprimatologie, Paléontologie Humaine: Evolution et Paléoenvironnements, UMR 7262 CNRS, Université de Poitiers, 86000, France;3. Centre de Recherches Pétrographiques et Géochimiques, UMR CNRS 7358, Vandoeuvre-lès-Nancy 54500, France;4. Université Pierre et Marie Curie, CR2P, MNHN, UPMC-Paris6, 57 rue Cuvier, CP 48, F-75005, Paris, France;5. Muséum national d''Histoire naturelle, CR2P — CNRS, MNHN, UPMC-Paris6, 57 rue Cuvier, CP 38, F-75005, Paris, France;6. Senckenberg Research Institute, Frankfurt Main / Steinmann Institute, University of Bonn, Nussallee 8, 53115 Bonn, Germany;7. Department of Geology, Hinthada University, Hinthada Township, Myanmar;1. Department of Electronics and Communication Engineering, Dr. B. C. Roy Engineering College, Durgapur 713206, India;2. Department of Applied Electronics and Instrumentation Engineering, Dr. B. C. Roy Engineering College, Durgapur 713206, India;3. Department of Mathematics, University Institute of Technology, University of Burdwan, Burdwan 713104, India;4. Department of Electronics and Communication Engineering, National Institute of Technology, Durgapur 713209, India |
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| Abstract: | In one-dimensional chaotic dynamics, a global multifractal relation between topological entropies and fractal dimensions of arbitrary period-p-tupling attractors is analyzed on all critical (accumulation) points of transitions to chaos, where the Lyapunov characteristic exponent is zero. The global metric regularity of topological entropies versus fractal dimensions is well characterized by the self-similarity. By the fractal interpolation based on the iterated function system, the fractal dimensions of the curves of topological entropies versus capacity dimensions and versus information dimensions are both found to be 1.82. |
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