Energy Transfer in a Fast-Slow Hamiltonian System

  • Dmitry Dolgopyat
  • Carlangelo LiveraniEmail author


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.


Manifold Invariant Measure Negative Curvature Limit Equation Martingale Problem 
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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Dipartimento di MatematicaII Università di Roma (Tor Vergata), Via della Ricerca ScientificaRomaItaly

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