Journal ArticleDOI
Integrability of hamiltonian systems on cantor sets
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This article is published in Communications on Pure and Applied Mathematics.The article was published on 1982-09-01. It has received 348 citations till now. The article focuses on the topics: Hamiltonian system & Kolmogorov–Arnold–Moser theorem.read more
Citations
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Journal ArticleDOI
Frequency analysis for multi-dimensional systems: global dynamics and diffusion
TL;DR: Frequency analysis is a new method for analyzing the stability of orbits in a conservative dynamical system as discussed by the authors, which is a powerful method for analysis weakly chaotic motion in Hamiltonian systems or symplectic maps.
Journal ArticleDOI
Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
TL;DR: In this paper, the nonlinear wave equation was studied for a large class of potentials, and it was shown that for each potential, one can use KAM methods to construct periodic and quasi-periodic solutions.
Posted Content
A lecture on the classical KAM theorem
TL;DR: In this paper, the KAM theorem is described in its most basic form and a complete and detailed proof is given, and the emphasis is more on the underlying ideas than on the sharpness of the arguments.
References
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Book
Singular Integrals and Differentiability Properties of Functions.
TL;DR: Stein's seminal work Real Analysis as mentioned in this paper is considered the most influential mathematics text in the last thirty-five years and has been widely used as a reference for many applications in the field of analysis.
Book
Lectures on Celestial Mechanics
TL;DR: The three-body problem was studied in this paper, where Covarinace of Lagarangian Derivatives and Canonical Transformation were applied to the problem of estimating the perimeter and the velocity of the system.
Approximation of Functions of Several Variables and Embedding Theorems
TL;DR: The theory of embeddings of classes of differentiable functions of several variables has been intensively expanded during the past two decades, and a number of its fundamental problems have been resolved as discussed by the authors.
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Proof of a theorem of a.?n.?kolmogorov on the invariance of quasi-periodic motions under small perturbations of the hamiltonian
TL;DR: In this paper, the rotatory motion of a heavy asymmetric rigid body is studied and the theorems of the rotational motion of such a rigid body are formulated and proved.