Energy transfer in a fast-slow Hamiltonian system

Dmitry Dolgopyat; Carlangelo Liverani

doi:10.1007/s00220-011-1317-7

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arXiv · 1010.3972

Energy transfer in a fast-slow Hamiltonian system

Dmitry Dolgopyat·Carlangelo Liverani

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Abstract

We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a non linear diffusion equation. This is a first step toward the derivation of macroscopic equations from a Hamiltonian microscopic dynamics in the case of weakly coupled systems.

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Dmitry Dolgopyat, Carlangelo Liverani. 2011-04-10. Energy transfer in a fast-slow Hamiltonian system. https://doi.org/10.1007/s00220-011-1317-7

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