On the number of ergodic minimizing measures for Lagrangian flows
Radu Saghin - Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON M5S2E4, Canada (email)
We give an example where for an open set of Lagrangians on the n-torus there is at least one cohomology class c with at least n different ergodic c-minimizing measures. One of the problems posed by Ricardo Mañé in his paper 'Generic properties and problems of minimizing measures of Lagrangian systems' (Nonlinearity, 1996) was the following:
Keywords: Lagrangian systems, Action-minimizing measures.
Received: September 2005; Revised: September 2006; Published: December 2006.
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