Energy Transfer in a Fast-Slow Hamiltonian System |
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Authors: | Dmitry Dolgopyat Carlangelo Liverani |
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Affiliation: | 1.Department of Mathematics,University of Maryland,College Park,USA;2.Dipartimento di Matematica,II Università di Roma (Tor Vergata), Via della Ricerca Scientifica,Roma,Italy |
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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 nonlinear 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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