Quantitative Universality for a Class of Weakly Chaotic Systems

  title={Quantitative Universality for a Class of Weakly Chaotic Systems},
  author={Roberto Venegeroles},
  journal={Journal of Statistical Physics},
We consider a general class of intermittent maps designed to be weakly chaotic, i.e., for which the separation of trajectories of nearby initial conditions is weaker than exponential. We show that all its spatio and temporal properties, hitherto regarded independently in the literature, can be represented by a single characteristic function ϕ. A universal criterion for the choice of ϕ is obtained within the Feigenbaum’s renormalization-group approach. We find a general expression for the… Expand
6 Citations
Number of first-passage times as a measurement of information for weakly chaotic systems.
It is shown that, for individual trajectories, information can be accurately inferred by the number of first-passage times through a given turbulent phase-space cell, which enables us to calculate far more efficiently Lyapunov exponents for such systems. Expand
Exact invariant measures: How the strength of measure settles the intensity of chaos.
  • Roberto Venegeroles
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
It is given a simple proof that infinite measure implies universal Mittag-Leffler statistics of observables, rather than narrow distributions typically observed in finite measure ergodic maps. Expand
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Explicit Time-Dependent Entropy Production Expressions: Fractional and Fractal Pesin Relations
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A Complete Bibliography of the Journal of Statistical Physics: 2000{2009
(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1Expand


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This book chapter introduces to the concept of weak chaos, aspects of its ergodic theory description, and properties of the anomalous dynamics associated with it. In the first half of the chapter weExpand
Lyapunov statistics and mixing rates for intermittent systems.
It is demonstrated that a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems fails for a generic class of maps of the Pomeau-Manneville type. Expand
Torus fractalization and intermittency.
  • S. Kuznetsov
  • Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
The bifurcation transition is studied for the onset of intermittency analogous to the Pomeau-Manneville mechanism of type I, but generalized for the presence of a quasiperiodic external force. TheExpand
Quantitative universality for a class of nonlinear transformations
AbstractA large class of recursion relationsxn + 1 = λf(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. TheExpand
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It is found that the adoption of a nonextensive approach does not serve any predictive purpose: It does not even signal a transition from a stationary to a nonstationary regime. Expand
Pesin’s Relation for Weakly Chaotic One-Dimensional Systems
We explore a recent rigorous result due to Zweimuller in order to propose an extension, for the case of weakly chaotic systems, of the usual Pesin’s relation between the Lyapunov exponent and theExpand
Chaotic Hamiltonian systems: survival probability.
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  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
New semiphenomenological arguments are presented which enable us to map the dynamical system near the chaos border onto the effective "ultrametric diffusion" on the boundary of a treelike space with hierarchically organized transition rates. Expand
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  • P. Gaspard, X. Wang
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1988
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We investigate ergodic properties of a one-dimensional intermittent map that has not only an indifferent fixed point but also a singular structure such that a uniform measure is invariant underExpand
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We address here the problem of extending the Pesin relation among positive Lyapunov exponents and the Kolmogorov–Sinai entropy to the case of dynamical systems exhibiting subexponentialExpand