Two-day workshop on Dynamical Systems (Friday, 30th November 2018)
Starts 30 Nov 2018 09:30
Ends 30 Nov 2018 12:00
Central European Time
Leonardo Building - Luigi Stasi Seminar Room
9:30 - 10:30 Lucia Simonelli (ICTP) On Renormalization in Parabolic Dynamics
We give an introduction to parabolic dynamics and the relevant properties that can be proved through renormalization techniques. We describe in detail the Heisenberg nilflow renormalized by a partially hyperbolic automorphism of the nilmanifold. Through this renormalization it can be shown that the spectrum of the transfer operator of the partially hyperbolic map gives information about the (parabolic) nilflow, in particular, estimates for the deviation of ergodic averages. This talk is based on joint work with Oliver Butterley.
10:30 - 11:00 break
11:00 - 12:00 Lorenzo J. Diaz (PUC, Rio de Janeiro) Prescribed averages and construction of non-hyperbolic ergodic measures
The setting is a transitive diffeomorphism and a continuous potential taking positive and negative values. We will discuss methods for constructing "interesting" orbits with prescribed averages for that potential and apply the results for the construction of nonhyperbolic ergodic measures.