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Universality of algebraic laws in hamiltonian systems.
This work conjecture the universal exponents gamma=beta=3/2 for trapping of trajectories to regular islands based on analytical results for a wide class of area-preserving maps. Expand
Non-Gaussian features of chaotic Hamiltonian transport
Some non-Gaussian aspects of chaotic transport are investigated for a general class of two-dimensional area-preserving maps. Kurtosis, in particular, is calculated from the diffusion and the BurnettExpand
Calculation of superdiffusion for the Chirikov-Taylor model.
A differential form for the Perron-Frobenius evolution operator is introduced in which normal diffusion and superdiffusion are treated separately through phases formed by angular wave numbers, resulting in a Schloemilch series with an exponent beta=3/2 for the divergences. Expand
Alternative numerical computation of one-sided Lévy and Mittag-Leffler distributions.
It is shown that α≈0.567 and 0.605 correspond, respectively, to the one-sided Lévy and Mittag-Leffler distributions with shortest maxima, and how these results can elucidate some recently described dynamical behavior of intermittent systems is discussed. Expand
Leading pollicott-ruelle resonances and transport in area-preserving maps.
The leading Pollicott-Ruelle resonance is calculated analytically for a general class of two-dimensional area-preserving maps, and a new effect emerges: the angular evolution can induce fast or slow modes of diffusion even in the high stochasticity regime. Expand
A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity.
A nonlinear mathematical model of cancer immunosurveillance that takes into account some of these features based on cell-mediated immune responses, and describes phenomena that are seen in vivo, such as tumor dormancy, robustness, immunoselection over tumor heterogeneity and strong sensitivity to initial conditions in the composition of tumor microenvironment. Expand
Quantitative Universality for a Class of Weakly Chaotic Systems
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 thatExpand
Thermodynamic phase transitions for Pomeau-Manneville maps.
  • Roberto Venegeroles
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and…
  • 14 August 2012
A distributional limit theorem is used to provide both a powerful tool for calculating thermodynamic potentials as also an understanding of the dynamic characteristics at each instability phase of Pomeau-Manneville intermittent maps. Expand
Pesin-type relation for subexponential instability
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
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