Supperdiusion constants for certain nonuniformly hyperbolic systems
- Series
- CDSNS Colloquium
- Time
- Monday, October 24, 2016 - 11:06 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Hongkun Zhang – U. Mass Amherst
We investigate deterministic superdiusion in nonuniformly hyperbolic system
models in terms of the convergence of rescaled distributions to the normal
distribution following the abnormal central limit theorem, which differs
from the usual requirement that the mean square displacement grow
asymptotically linearly in time. We obtain an explicit formula for the
superdiffusion constant in terms of the ne structure that originates in the
phase transitions as well as the geometry of the configuration domains of
the systems. Models that satisfy our main assumptions include chaotic
Lorentz gas, Bunimovich stadia, billiards with cusps, and can be apply to
other nonuniformly hyperbolic systems with slow correlation decay rates of
order O(1/n)