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2004•Ergodic Theory and Dynamical SystemsRequires access

Remarks on stability and diffusion in high-dimensional Hamiltonian systems and partial differential equations

Jean Bourgain

Open publisher page 62 citations

Abstract

This is a partial survey of various developments of the classical KAM theory in dynamical systems to infinite-dimensional lattice models and Hamiltonian PDEs. Particular emphasis is given on Nekhoroshev stability and growth of higher Sobolev norms. Some new results are also presented.

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What this paper is about

This is a partial survey of various developments of the classical KAM theory in dynamical systems to infinite-dimensional lattice models and Hamiltonian PDEs. Particular emphasis is given on Nekhoroshev stability and growth of higher Sobolev norms. Some new results are also presented.

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OpenAlex reports 62 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This is a partial survey of various developments of the classical KAM theory in dynamical systems to infinite-dimensional lattice models and Hamiltonian PDEs. Particular emphasis is given on Nekhoroshev stability and growth of higher Sobolev norms. Some new results are also presented.

Key concepts: Mathematics, Hamiltonian system, Sobolev space, Partial differential equation, Dynamical systems theory, Mathematical analysis, Hamiltonian (control theory), Stability (learning theory)

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