Routes to chaos,universality and glass formation |
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| Institution: | 1. Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan;2. Institut für Baustoffe, HIF E12, ETH Hönggerberg, CH-8093 Zürich, Switzerland;1. Dartmouth College, Hanover, NH, United States;2. Intel Corporation, Hillsboro, OR, United States;3. Princeton University, Princeton, NJ, United States;4. DeepMind, London, UK;5. Columbia University, New York, NY, United States;1. School of Engineering, Institute for Digital Communications, University of Edinburgh, Edinburgh EH9 3FB, UK;2. Department of Mathematics, University Carlos III de Madrid, Avda. de la Universidad 30, 28911, Leganés (Madrid), Spain;4. Fachbereich 4 – Mathematik, Universität Trier, 54286 Trier, Germany;1. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Roma, Italy;2. Scuola Normale Superiore, Pisa, Italy;3. Fachbereich Physik, Universität des Saarlandes, Saarbrücken, Germany;4. Max Planck Institute for Informatics, Saarbrücken, Germany;5. Max Planck Institute for Informatics and Fachbereich Informatik, Universität des Saarlandes, Germany;6. École Normale Supérieure, Paris, France |
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| Abstract: | We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these situations the dynamical behavior is exactly describable through infinite families of Tsallis’ q-exponential functions. Furthermore, the addition of a noise perturbation to the dynamics at the onset of chaos of the logistic map allows to establish parallels with the behavior of supercooled liquids close to glass formation. Specifically, the occurrence of two-step relaxation, aging with its characteristic scaling property, and subdiffusion and arrest is corroborated for such a system. |
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