We study the approach to near-equipartition in an N-dimensional FPU Hamiltonian. We investigate numerically the time evolution of orbits with initial energy in some few low-frequency linear modes. Our results indicate a transition where, above a critical energy, one can reach near-equipartition if one waits for a time proportional N2. Below this critical energy the time is exponentially long. We develop a theory to understand the time evolution and deformation of the actions of the oscillators based on a normal form treatment of the resonances among the oscillators. Our theory predicts the critical energy for near-equipartition, the time scale to near-equipartition and the deformation of the actions below equipartition, in qualitative agreement with the numerical results.
Title
TIME SCALE TO ERGODICITY IN THE FPU SYSTEM
Published
1993-11-01
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
ERL-93-92
Type
Text
Extent
46 p
Archive
The Engineering Library
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