Minimax probabilities for Aubry-Mather problems

Diogo A. Gomes, Nara Jung, Artur O. Lopes

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper, we study minimax Aubry-Mather measures and its main properties. We consider first the discrete time problem and then the continuous time case. In the discrete time problem, we establish existence, study some of the main properties using duality theory and present some examples. In the continuous time case, we establish both existence and non-existence results. First, we give some examples showing that in continuous time stationary minimax Mather measures are either trivial or fail to exist. A more natural definition in continuous time are T-periodic minimax Mather measures. We give a complete characterization of these measures and discuss several examples.

Original languageEnglish (US)
Pages (from-to)789-813
Number of pages25
JournalCommunications in Contemporary Mathematics
Issue number5
StatePublished - Oct 2010
Externally publishedYes


  • Aubry-Mather measures
  • Lagrangian cost
  • Minimax measures
  • discrete Aubry-Mather problem
  • duality
  • holonomic measures

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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