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Diffusion approximation and hyperbolic automorphisms of the torus. (English) Zbl 0902.35088

The goal of the present paper is to give an example of a reversible dynamics which after some appropriate scaling leads to an irreversible limit dynamics. In particular, the authors want to present such an example that allows for a complete and elementary analysis, without appeal to sophisticated tools from ergodic theory. The examples presented are hyperbolic automorphisms \(T\) of the torus, and for simplicity, they work with the two-dimensional torus and Arnold’s cat map. It is proven that a suitably scaled process converges weakly to a diffusion.
Reviewer: A.Bovier (Berlin)

MSC:

35Q35 PDEs in connection with fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
60J60 Diffusion processes
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