Effective Hamiltonians and averaging for Hamiltonian dynamics II

L. C. Evans*, D. Gomes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

We extend to time-dependent Hamiltonians some of the PDE methods from our previous paper [E-G1], and in particular the theory of "effective Hamiltonians" introduced by LIONS, PAPANICOLAOU & VARADHAN [L-P-V]. These PDE techniques augment the variational approach of MATHER [Mt1,Mt2,Mt3,Mt4,M-F] and the weak KAM methods of FATHI [F1,F2,F3,F4,F5]. We also provide a weak interpretation of adiabatic invariance of the action and suggest a formula for the Berry-Hannay geometric phase in terms of an effective Hamiltonian.

Original languageEnglish (US)
Pages (from-to)271-305
Number of pages35
JournalArchive for Rational Mechanics and Analysis
Volume161
Issue number4
DOIs
StatePublished - Mar 2002
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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