Effective Hamiltonians and averaging for Hamiltonian dynamics I

L. C. Evans, Diogo Gomes

Research output: Contribution to journalArticlepeer-review

74 Scopus citations

Abstract

This paper, building upon ideas of Mather, Moser, Fathi, E and others, applies PDE (partial differential equation) methods to understand the structure of certain Hamiltonian flows. The main point is that the "cell" or "corrector" PDE, introduced and solved in a weak sense by Lions, Papanicolaou and Varadhan in their study of periodic homogenization for Hamilton-Jacobi equations, formally induces a canonical change of variables, in terms of which the dynamics are trivial. We investigate to what extent this observation can be made rigorous in the case that the Hamiltonian is strictly convex in the momenta, given that the relevant PDE does not usually in fact admit a smooth solution.

Original languageEnglish (US)
Pages (from-to)1-33
Number of pages33
JournalArchive for Rational Mechanics and Analysis
Volume157
Issue number1
DOIs
StatePublished - Mar 20 2001

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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