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arXiv · 2207.03981

Perturbation of Systems with a First Integral: Motion on the Reeb Graph

Mark Freidlin
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Abstract

We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to some extent, turns out to be universal: it is determined by the first integral, the deterministic perturbation, and the initial point. Furthermore, it is the same for a broad class of noises. In particular, the long-time behavior of a deterministic system can, in a sense, be stochastic and stochastic systems can have a reduced stochasticity. The limiting distribution is calculated explicitly.

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Mark Freidlin. 2022-07-08. Perturbation of Systems with a First Integral: Motion on the Reeb Graph. https://doi.org/10.1007/s10955-022-02995-3

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