Abstract
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 language | English (US) |
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Pages (from-to) | 789-813 |
Number of pages | 25 |
Journal | Communications in Contemporary Mathematics |
Volume | 12 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2010 |
Externally published | Yes |
Bibliographical note
Funding Information:D. Gomes was partially supported by the Center for Mathematical Analysis, Geometry and Dynamical Systems through FCT Program POCTI/FEDER and also by grant DENO/FCT-PT (PTDC/EEA-ACR/67020/2006). A. O. Lopes was partially supported by CNPq, PRONEX — Sistemas Dinâmicos, Instituto do Milênio, and is beneficiary of CAPES financial support.
Keywords
- Aubry-Mather measures
- Lagrangian cost
- Minimax measures
- discrete Aubry-Mather problem
- duality
- holonomic measures
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics