Stochasticity in Deterministic Systems
Chaotic dynamics gives rise to apparent randomness in deterministic systems. A natural question is the stochasticity of time series from such systems.
This presentation surveys recent results in ergodic theory which apply to large classes of systems including Henon and Lorenz attractors. Applications range from (1) classical examples in Mathematical Physics: Lorentz gases as deterministic models for stochastic behaviour; to (2) pattern forming excitable media: hypermeander of spiral waves where the spiral tip appears to undergo a random walk in the plane.
For (1), Nicol and the speaker proved recently that the positions of almost all gas molecules behave asymptotically like sample paths of Brownian motion. For (2), a mechanism (and experiment) is proposed for mathematically verifiable Brownian-like motion for the spiral tip.
Ian Melbourne, University of Surrey, United Kingdom