Colloquium Mathematics: Dr. A.E. Sterk, University of Groningen

Title: Predictability of rare events in dynamical systems

Abstract:
In deterministic dynamical systems the initial condition completely determines the future evolution of the system. However, since the seminal work of E.N. Lorenz (1917-2008) it is well known that even deterministic systems can be unpredictable: small errors in the initial condition can grow exponentially in time. This phenomenon, now known colloquially as the butterfly effect, fundamentally limits the accuracy of long-term weather forecasts and stimulated mathematical research on nonlinear dynamics and chaos theory.

Predictability indicators like the Lyapunov exponent measure the predictability of the system as a whole. However, predictability should depend on the event one wants to predict. In this talk I will discuss a method for quantifying the predictability of the event that the evolution of a deterministic dynamical system enters a specific subset of state space at a given lead time. The main idea is to study the distribution of finite-time growth rates of errors in initial conditions along the state space of the system. Comparing error growth rates of initial conditions leading to an event with all possible growth rates then gives a measure of the predictability of the event. The method will be illustrated by means of simple toy models.

Colloquium coordinators are Prof.dr. A.J. van der Schaft ( a.j.van.der.schaft rug.nl ) and Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/