快-慢哈密顿系统中的能量传递
Energy transfer in a fast-slow Hamiltonian system
摘要：
我们考虑一个有限区域的弱相互作用的测地线流的负曲率流形上的晶格，我们表明，当重新调整的相互作用和适当的时间，能量的流动演变根据非线性扩散方程。这是在弱耦合系统的情况下，从哈密顿微观动力学推导宏观方程的第一步。
英文摘要：
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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