BEGIN:VCALENDAR
PRODID:-//eluceo/ical//2.0/EN
VERSION:2.0
CALSCALE:GREGORIAN
BEGIN:VEVENT
UID:e78666f8fc066e201426948104196d68
DTSTAMP:20261009T030243Z
SUMMARY:Junior Dynamics Seminar – Ross Ah-Weng
DESCRIPTION:Statistical Degradation of Chaotic Dynamical Systems on Compute
 rs\nSpeaker: Ross Ah-Weng\nAbstract: Many chaotic physical systems are fo
 recasted using Birkhoff averages of observables along numerically simulate
 d trajectories. However\, when any dynamical system is simulated in floati
 ng-point arithmetic\, the continuum is replaced by a finite discrete domai
 n. The new dynamics are substantially different: every trajectory is event
 ually periodic\, sufficiently close trajectories become indistinguishable 
 after roundoff\, and any invariant measure is supported on a finite set of
  disjoint periodic orbits. We identify a generic mechanism in which non-in
 jectivity from rounding causes statistics inferred from any simulated traj
 ectory to continually and irreversibly degrade. We develop this framework 
 using the formalism of functional graphs\, the Perron-Frobenius Operator\,
  and derive general error bounds on observables. We validate this framewor
 k numerically on the Logistic map and various parameters of the Generalise
 d Bernoulli Map\, at increasing precision up to IEEE 754 FP32. In the case
  of stochastic rounding\, we construct the associated Markov Chain and com
 ment on a failure mode associated to exactly representable periodic orbits
 . Finally\, we empirically test convergence properties from an initial uni
 form distribution\, and find evidence that Birkhoff averages over finite t
 imespans on computers consistently outperform the infinite time limit.
URL:https://www.imperial.ac.uk/events/214783/junior-dynamics-seminar-ross-a
 h-weng/
DTSTART;TZID=Europe/London:20261015T160000
DTEND;TZID=Europe/London:20261015T170000
LOCATION:642\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
DTSTART:20261015T160000
TZNAME:BST
TZOFFSETTO:+0100
TZOFFSETFROM:+0100
END:DAYLIGHT
END:VTIMEZONE
END:VCALENDAR