相关论文: Maximal tori in infinite-dimensional Hamiltonian s…

We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We…

This paper investigates the effect of random perturbations, in particular multiplicative noise, on the integrable structure of Hamiltonian systems, with a particular focus on KAM theory for stochastic Hamiltonian dynamics. We prove that,…

We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group.…

It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it…

We proved the existence of invariant tori in differentiable Hamiltonian vector fields without action-angle variables. It is a generalization of the result of [Llave, 2005] that deals with analytic vector fields.

In this paper, we study the Melnikov's persistence for completely degenerate Hamiltonian systems with the following Hamiltonian \begin{equation*} H(x,y,u,v)=h(y)+g(u,v)+\varepsilon P(x,y,u,v),~~~(x,y,u,v)\in \mathbb{T}^n\times{G}\times…

This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which…

Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that transport the symplectic form into a multiple of itself (with a…

We prove the existence of invariant tori to the area-preserving maps defined on $ \mathbb{R}^2\times\mathbb{T} $ \begin{equation*} \bar{x}=F(x,\theta), \qquad \bar{\theta}=\theta+\alpha\, \,(\alpha\in \mathbb{R}\setminus\mathbb{Q}),…

In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to…

In this paper, we prove the existence of full dimensional invariant tori for a non-autonomous, almost-periodically forced nonlinear beam equation with a periodic boundary condition via KAM theory.

We give an explicit arithmetical condition which guarantees the existence of the unstable manifold of the MacKay approximate renormalisation scheme for the breakup of invariant tori in one and a half degrees of freedom Hamiltonian systems,…

We show that in the neighborhood of each ``finite type'' singular orbit of a real analytic integrable dynamical system (hamiltonian or not) there is a real analytic torus action which preserves the system and which is transitive on this…

In 2004, F\'ejoz [D\'emonstration du 'th\'eor\'eme d'Arnold' sur la stabilit\'e du syst\`eme plan\'etaire (d'apr\`es M. Herman). Ergod. Th. & Dynam. Sys. 24(5) (2004), 1521-1582], completing investigations of Herman's [D\'emonstration d'un…

In this paper, we prove a KAM theorem in a-posteriori format, using the parameterization method to look invariant tori in non-autonomous Hamiltonian systems with $n$ degrees of freedom that depend periodically or quasi-periodically (QP) on…

What kinds of motion can occur in classical mechanics? We address this question by looking at the structures traced out by trajectories in phase space; the most orderely, completely integrable systems, are charactrized by phase trajectories…

We revisit the famous Nos\'e-Hoover system in this paper and show the existence of some averagely conservative regions which are filled with an infinite sequence of nested tori. Depending on initial conditions, some invariant tori are of…

Two classes of two-dimensional time-periodic systems of ordinary differential equations with a small parameter e in the perturbed part, which is continuous and, for $\varepsilon=0$, analytic in zero, are studied. Depending on the presence…

In this article, we consider the dynamics in a neighborhood of a quasi-periodic torus which is invariant by a Hamiltonian flow, we discuss several notions of stability and we prove several results of instability when the frequency of the…

We prove that exists a Lindstedt series that holds when a Hamiltonian is driven by a perturbation going to infinity. This series appears to be dual to a standard Lindstedt series as it can be obtained by interchanging the role of the…