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Infinite horizon variational problems and dissipative systems

We give a sharp estimate for the discount rate that guarantees smooth optimal syntheses of infinite horizon variational problems with "mechanical Lagrangians". These syntheses describe a long time behavior of dissipative mechanical systems with a sufficiently strong dissipation. If time permits, we’ll also discuss some observations that concern a weaker dissipation.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46