Journal ArticleDOI
On Elliptic Lower Dimensional Tori in Hamiltonian Systems.
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This article is published in Mathematische Zeitschrift.The article was published on 1989-12-01. It has received 276 citations till now. The article focuses on the topics: Hamiltonian system & Partial differential equation.read more
Citations
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Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
Robert S. MacKay,Serge Aubry +1 more
TL;DR: In this paper, the existence of time-periodic, spatially localized solutions for weakly coupled oscillators is proved for a broad range of time reversible or Hamiltonian networks.
Journal ArticleDOI
Newton's method and periodic solutions of nonlinear wave equations
Walter Craig,C. Eugene Wayne +1 more
TL;DR: In this paper, the existence of periodic solutions of the nonlinear wave equation was proved, provided that the coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation.
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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.
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Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrodinger equation
Sergej B. Kuksin,Jürgen Pöschel +1 more
TL;DR: In this article, the authors were guests of the Forschungsinstitut fur Mathematik at the ETH Zurich, and they thank the institute for its hospitality, pleasant working atmosphere and helpful staff.
Journal ArticleDOI
Quasi-periodic solutions of hamiltonian perturbations of 2d linear schrodinger equations
TL;DR: In this paper, the authors considered the problem of the persistency of quasi-periodic solutions of linear or integrable equations after Hamiltonian perturbation in the case of Dirichlet boundary conditions.
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.