Sensitive Chaotic Systems

Viviane Baladi is currently professor at the Institut de Mathématiques de Jussieu, CNRS, Paris. Thanks to a grant from the Knut and Alice Wallenberg Foundation, she will be Visiting Professor at the Centre for Mathematical Sciences, Lund University, Sweden.

It is well known that despite improvements to mathematical models, long-term weather forecasting is difficult. The reason is that the outcomes of the time development of weather and other chaotic systems are extremely sensitive to the initial conditions. The metaphor for this dependence is popularly known as the butterfly effect; a butterfly’s wing flapping in Brazil may result in a storm over the Atlantic Ocean.

Chaos theory has already developed tools for analyzing the long-term evolution of many sensitive chaotic systems, but such studies result only in the most likely long-term outcomes, which are described using a “physical measure”. How this measure responds to minor changes in the system is described by the theory of response used for climate predictions, and other areas beyond mathematics.

Viviane Baladi, a world-leading researcher in this field, has recently studied billiards, particles moving in an area of a certain shape; the analogy is that of the balls on a billiard table. This is a classic example of a dynamic system that, for some forms on the billiard table, gives rise to chaotic dynamics. To address these issues, new analytical methods are being developed.

Lund has a strong environment that focuses on studies of dynamic systems. Baladi’s stay there will further strengthen this environment through new research collaborations and doctoral courses.