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Invariant measure selection by noise. An example

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  • We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on the specifics of the stochastic forcing.
    Mathematics Subject Classification: Primary: 60H10, 37L40; Secondary: 37A60, 34C29.

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