On the number of ergodic minimizing measures for Lagrangian flows
Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON M5S2E4, Canada
Is it true that for generic Lagrangians every minimizing measure is uniquely ergodic?
A weaker statement is that for generic Lagrangians every cohomology class has exactly one minimizing measure, which of course will be ergodic. Our example shows that this can't be true and as a consequence one can hope to prove at most that for a generic Lagrangian, for every cohomology class there are at most n corresponding ergodic minimizing measures, where n is the dimension of the first cohomology group.
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