Junior Dynamics Seminar – Ross Ah-Weng

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Statistical Degradation of Chaotic Dynamical Systems on Computers Speaker: Ross Ah-Weng Abstract: Many chaotic physical systems are forecasted using Birkhoff averages of observables along numerically simulated trajectories. However, when any dynamical system is simulated in floating-point arithmetic, the continuum is replaced by a finite discrete domain. The new dynamics are substantially different: every trajectory is eventually periodic, sufficiently close trajectories become indistinguishable after roundoff, and any invariant measure is supported on a finite set of disjoint periodic orbits…