There are two parts to this talk. In the first part, I will explain the idea of SRB measures for chaotic attractors as the analog of Liouville measure for Hamiltonian systems. SRB measures were discovered for Axiom A attractors by Sinai, Ruelle and Bowen in the 1970s. Even though their role is taken for granted in physics, proving rigorously the existence of these invariant measures outside of the Axiom A category poses serious analytical challenges. The main examples so far have come from attractors that are only mildly chaotic, in the sense that they have only a single direction of instability. An example of such an attractor is the periodically kicked linear shear flow. In the second half of this lecture, I will describe a few other examples of shear-induced chaos, a phenomenon that occurs easily in the periodic kicking of general limit cycles, and of systems undergoing Hopf bifurcations, in ODEs as well as in some PDEs.
Samstag, den 28. Oktober 2017 um 11.30-12.30 Uhr, in Mathematikon, INF 205, Konferenzraum, 5. OG Samstag, den 28. Oktober 2017 at 11.30-12.30, in Mathematikon, INF 205, Konferenzraum, 5. OG
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers