Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy...
Out of equilibrium magnetised solutions of the XY-Hamiltonian Mean Field (XY-HMF) model are build using an ensemble of integrable uncoupled pendula. Using...
Transport of a particle in a spatially periodic harmonic potential under the influence
of a slowly time-dependent unbiased periodic external force is studied....
Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems:
We investigate the dynamics of...
Romain Bachelard, Cristel Chandre, Duccio Fanelli, Xavier Leoncini, Michel Vittot, Stabilizing the intensity for a Hamiltonian model of the FEL, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 593, 1-2 (2008) 94-97
The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles, as in a Free Electron Laser, displays large...
Short description: This book collects lecture notes and contributions
presented during the CCT'07 conference (Marseilles June 2007).
Areas covered range from...
The saturated dynamics of a Single-Pass Free Electron Laser is considered within a simplified mean-field approach. A method is proposed to increase the size of...
We investigate the multiphoton ionization of hydrogen driven by a strong bichromatic microwave field. In a regime where classical and quantum simulations...
Transport and mixing properties of passive particles advected by an
array of vortices are investigated. Starting from the integrable case,
it is shown that a...
The ExB drift motion of charged test particle dynamics in the Scrape-Off-Layer (SOL) is analyzed to investigate a transport control strategy based on...
The multiphoton ionization of hydrogen by a strong bichromatic
microwave field is a complex process prototypical for atomic
control research. Periodic orbit...
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of...
The advection of passive tracers in an oscillating vortex chain is investigated. It is shown that by adding a suitable perturbation to the ideal flow, the...
We formulate a fictitious-time-flow equation which drives an initial guess torus to a torus invariant under a given dynamics, provided such a torus exists. The...
We present a control procedure to reduce the stochastic ionization of hydrogen atom in a strong microwave field by adding to the original Hamiltonian a...
A numerical method is proposed in order to track field lines of three-dimensional divergence free fields. Field lines are computed by a locally valid...
The multiphoton ionization of hydrogen atoms in a strong elliptically polarized microwave field exhibits complex features that are not observed for ionization...
In this article we present an application of a method of control of Hamiltonian systems to the chaotic velocity diffusion of a cold electron beam interacting...
We present a method of control which is able to create barriers to magnetic field line diffusion by a small modification of the magnetic perturbation. This...
The structure and geometry of high-dimensional, complex dynamical sys-
tems is usually hidden under a profusion of numerical data. We show that time-frequency...
In this paper, we present a model describing the time evolution of twodimensional
surface waves in gravity and infinite depth. The model of six
interacting...
The structure and geometry of high-dimensional, complex dynamical systems is usually hidden under a profusion of numerical data. We show that time-frequency...
We describe a method of control of chaos that occurs in area-preserving maps. This method is based on small modifications of the original map by addition of a...
We present a method to control transport in Hamiltonian systems. We provide an algorithm - based on a perturbation of the original Hamiltonian localized in...
We review a method of control for Hamiltonian systems which is able to create smooth invariant tori. This method of control is based on an apt modification of...
Chaotic diffusion often represents a severe obstacle for the setup of experiments, e.g., in fusion plasmas or particle accelerators. We present a complete test...
Transport properties of particles evolving in a system
governed by the Charney-Hasegawa-Mima equation are investigated. Transport
is found to be anomalous with...
We report an analysis of intramolecular dynamics of the highly excited planar carbonyl sulfide below and at the dissociation threshold by the fast Lyapunov...
It is shown that a relevant control of Hamiltonian chaos is possible through suitable small perturbations whose form can be explicitly computed. In particular,...
We present a technique to control chaos in Hamiltonian systems which are close to integrable.By adding a small and simple control term to the perturbation, the...
We present a method of localised control of chaos in Hamiltonian systems. The aim is to modify the perturbation locally by a small control term which makes the...
Advection properties of passive particles in flows generated by point vortices are considered. Transport properties are anomalous with characteristic transport...
We consider a perturbation of an ``integrable'' Hamiltonian and give
an expression for the canonical or unitary transformation which
``simplifies'' this...
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory...
Xavier Leoncini, George M. Zaslavsky, Chaotic Jets, Communications in Nonlinear Science and Numerical Simulation 8, 265 (2003)
The problem of characterizing the origin of the non-Gaussian properties of transport resulting from Hamiltonian dynamics is addressed. For this purpose the...
We study the Floquet Hamiltonian \( -i\partial _{t} + H + V(\omega t)
\), acting in \linebreak \( L^{2}([\, 0,T\, ],\mathcal{H} ,dt) \), as
depending on the...
We analyze the classical phase space of the hydrogen atom in crossed magnetic and circularly polarized microwave fields in the high frequency regime, using the...
We consider the break-up of invariant tori in Hamiltonian systems with two degrees of freedom with a frequency which belongs to a cubic field. We define and...
We find that chaos in the stochastic ionization problem develops through the break-up of a sequence of noble tori. In addition to being very accurate, our...
We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of...
We construct an approximate renormalization for Hamiltonian systems with two degrees of freedom in order to study the break-up of invariant tori with arbitrary...
We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to...
We analyze by a renormalization method, the dynamics of a particle in a infinite square-well potential driven by an external monochromatic field. This method...
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and...
Dynamical and statistical properties of tracer advection are studied in a family of flows produced by three point-vortices of different signs. A collapse of...
Using the KAM method, we exhibit some solutions of a finite-dimensional approximation of the Zakharov Hamiltonian formulation of
gravity water waves, which are...
We construct an approximate renormalization transformation for Hamiltonian systems with three degrees of freedom in order to study the break-up of invariant...
A system of three point vortices in an unbounded plane has a special family of self-similarly contracting or expanding solutions: during the motion, vortex...
We consider a perturbed Floquet Hamiltonian $-i\partial_t + H + \beta
V(\omega t)$ in the Hilbert space $L^2([0,T],\mathcal{H},dt)$. Here
$H$ is a self-adjoint...
We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze...
We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser...
We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. The...
We give a proof of the KAM theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring's approach for Hamiltonians...
In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of...
We analyze the breakup of invariant tori in Hamiltonian systems with two degrees of freedom using a
combination of Kolmogorov-Arnold-Moser ~KAM! theory and...
A Hamiltonian dynamics is defined for the XY model by adding a kinetic energy term. Thermodynamical properties (total energy, magnetization, vorticity) derived...
We study an example of a perturbed Floquet Hamiltonian $K + \beta V$
depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is
pure point and...
We consider here two discrete versions of the modified KdV equation. In one
case, some solitary wave solutions, Backlund transformations and integrals
of...
We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group...
We propose a new framework based upon non commutative geometry to
control the semi classical limit in phase space. It leads in
particular to uniform estimates...