## 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

### Keywords:

irreversibility; Arnold’s cat map; dynamical systems
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### References:

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