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Related papers: Fast Arnold's diffusion in isochronous systems

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Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

Methodology · Statistics 2017-04-03 Nina Munkholt Jakobsen , Michael Sørensen

We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through…

Statistical Mechanics · Physics 2009-11-10 Freddy Bouchet , Fabio Cecconi , Angelo Vulpiani

Local integrability of hyperbolic oscillators is discussed to provide an introductory example of the Arnold's diffusion phenomenon in a forced pendulum. This is a text prepared for the the ISI summer school of June 1997 and deals with…

chao-dyn · Physics 2008-02-26 Giovanni Gallavotti

We consider a system of infinitely many penduli on an $m$-dimensional lattice with a weak coupling. For any prescribed path in the lattice, for suitable couplings, we construct orbits for this Hamiltonian system of infinite degrees of…

Dynamical Systems · Mathematics 2022-04-25 Filippo Giuliani , Marcel Guardia

A non self-similar change of coordinates provides improved matching asymptotics of the solutions of the fast diffusion equation for large times, compared to already known results, in the range for which Barenblatt solutions have a finite…

Analysis of PDEs · Mathematics 2011-12-20 Jean Dolbeault , Giuseppe Toscani

The aim of this paper is to discuss the constructivity of the method originally introduced by U. Bessi to approach the phenomenon of topological instability commonly known as Arnold's Diffusion. By adapting results and proofs from existing…

Dynamical Systems · Mathematics 2023-06-23 Alessandro Fortunati

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…

Probability · Mathematics 2021-06-08 Longjie Xie , Li Yang

We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + $\epsilon$H1($\theta$, p, t), $\theta$ $\in$ T n , p $\in$ B n , t $\in$ T = R/T be a nearly integrable system of arbitrary degrees of freedom n 2 with a strictly…

Dynamical Systems · Mathematics 2017-01-25 Patrick Bernard , K Kaloshin , K Zhang

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Statistics Theory · Mathematics 2007-06-13 Yacine Ait-Sahalia , Per A. Mykland

Global diffusion of Hamiltonian dynamical systems is investigated by using a coupled standard maps. Arnold web is visualized in the frequency space, using local rotation numbers, while Arnold diffusion and resonance overlaps are…

Chaotic Dynamics · Physics 2007-05-23 Seiichiro Honjo , Kunihiko Kaneko

The main model studied in this paper is a lattice of nearest neighbors coupled pendula. For certain localized coupling we prove existence of energy transfer and estimate its speed.

Dynamical Systems · Mathematics 2015-03-19 Vadim Kaloshin , Mark Levi , Marya Saprykina

We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient…

Statistical Mechanics · Physics 2015-03-20 R. M. S. Ferreira , M. V. S. Santos , C. C. Donato , J. S. Andrade , F. A. Oliveira

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…

Statistics Theory · Mathematics 2011-11-10 Yury A. Kutoyants , Nakahiro Yoshida

We study the problem of spin diffusion in magnetic systems without long-range order. We discuss the example of the 1D spin chain. For the system described by the Heisenberg Hamiltonian we show that there are no diffusive excitations.…

Condensed Matter · Physics 2007-05-23 Boris Narozhny

We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…

Other Condensed Matter · Physics 2007-05-23 Evzen Subrt , Petr Chvosta

We provide numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We show that even if a system is sufficiently close to be integrable, global diffusion occurs on a set…

Chaotic Dynamics · Physics 2007-05-23 Massimiliano Guzzo , Elena Lega , Claude Froeschle'

In the present paper we prove a strong form of Arnold diffusion. Let $\mathbb{T}^2$ be the two torus and $B^2$ be the unit ball around the origin in $\mathbb{R}^2$. Fix $\rho>0$. Our main result says that for a "generic" time-periodic…

Dynamical Systems · Mathematics 2018-04-10 Vadim Kaloshin , Ke Zhang

We prove the existence of diffusing solutions in the motion of a charged particle in the presence of an ABC magnetic field. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of…

Chaotic Dynamics · Physics 2016-12-21 Alejandro Luque , Daniel Peralta-Salas

We solve the anisotropic diffusion equation in 2D, where the dominant direction of diffusion is defined by a vector field which does not conform to a Cartesian grid. Our method uses operator splitting to separate the diffusion perpendicular…

Numerical Analysis · Mathematics 2023-03-29 Dean Muir , Kenneth Duru , Matthew Hole , Stuart Hudson

A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…

Mathematical Physics · Physics 2008-03-19 E. M. Beniaminov