Chaos in Partial Differential Equations

zbMath1043.35001arXiv0909.0910MaRDI QIDQ4458427

Y. Charles Li

Publication date: 17 March 2004

Full work available at URL: https://arxiv.org/abs/0909.0910

zbMATH Keywords

symbolic dynamicsKAM theoryGibbs measuresoliton equationSmale horseshoepersistence of invariant manifoldsMelnikov/Shilnikov analysisShadowing lemma

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Geometric theory, characteristics, transformations in context of PDEs (35A30) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

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