相关论文: A note on the KAM theorem for partially integrable…

We provide an arithmetic condition weaker then the Bryuno condition for which it is possible to apply a KAM scheme in dimension greater then one. The KAM scheme will be provided in the setting of linearization of analytic diffeomorphisms of…

In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of…

The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.

The aim of these notes is to present a self contained account of discrete weak KAM theory. Put aside the intrinsic elegance of this theory, it is also a toy model for classical weak KAM theory, where many technical difficulties disappear,…

We consider the persistence of smooth families of invariant tori in the reversible context 2 of KAM theory under various weak nondegeneracy conditions via Herman's method. The reversible KAM context 2 refers to the situation where the…

It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a…

In this article we show how one can use the local models of integrable Hamiltonian systems near critical points to prove a localization theorem for certain singular loci of integrables semi-toric systems for dimension greater than 4.

For an integrable Hamiltonian systems with $d$ degrees of freedom ($d\geq 2$), we consider quantitatively the existence and non-existence of the flow-invariant Lagrangian torus with given frequency under the perturbation beyond the scope of…

We investigate the existence of whiskered tori in some dissipative systems, called \sl conformally symplectic \rm systems, having the property that they transform the symplectic form into a multiple of itself. We consider a family $f_\mu$…

We adapt the Kolmogorov's normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant elliptic torus. As a byproduct, our procedure…

We observe that the so-called Generalised Equipartition Law for hamiltonian systems is actually valid only under specific hypotheses -- unfortunately omitted in some textbooks -- which limit its applicability when dealing with nonlinear…

It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…

For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…

In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…

This paper gives the most general form of the Adler-Kostant-Symes Theorem, and many applications of it, both finite and infinite dimensional, the former yielding algebraic completely integrable (a.c.i.) systems, and the latter examples in…

We introduce an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible Schr\"odinger systems. Using this KAM theorem together with partial Birkhoff normal form method, we find the existence of quasi-periodic…

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. We extend analytically the…

We study the existence of whiskered tori in a family $f_\mu$ of conformally symplectic maps depending on parameters $\mu$. Whiskered tori are tori on which the motion is a rotation, but they have as many expanding/contracting directions as…

The effect of quantum collapse and revival is a fascinating interference phenomenon. In this paper the phenomenon is demonstrated analytically and numerically for a simple system, a slightly anharmonic Hamiltonian. The initial wave-function…

We investigate the effective behaviour of a small transversal perturbation of order $\epsilon$ to a completely integrable stochastic Hamiltonian system, by which we mean a stochastic differential equation whose diffusion vector fields are…