Two-day workshop on Dynamical Systems: 28th and 30th November 2018 - ICTP Stasi Seminar Room

[ICTP Math Section]

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Two-day workshop on Dynamical Systems

28th and 30th November 2018 - Luigi Stasi seminar room (Leonardo da 
Vinci Building)
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Wednesday, 28 November 2018 (14:00 - 16:30)

14:00 - 15:00 Maria Jose Pacifico (UFRJ, Rio de Janeiro)
Lagrange spectrum of Lorenz attractors

We shall prove that the Lagrange spectrum of a geometric Lorenz 
attractor has non empty interior.

15:00 - 15:30    break

15:30 - 16:30 Katrin Gelfert (UFRJ, Rio de Janeiro)
Weak*, and in entropy, approximation of non-hyperbolic measures in 
partially hyperbolic diffeomorphisms

We consider certain partially hyperbolic non-hyperbolic diffeomorphisms 
with one-dimensional central bundle and study how non-hyperbolic ergodic 
measure (i.e. with zero central exponent) can be approximated in the 
weak* topology and in entropy by measures supported in basic sets with 
positive (negative) central Lyapunov exponent. Our method also allows to 
show how entropy changes "across" measures with central Lyapunov 
exponent close to zero. Besides the construction of ergodic theoretic 
skeletons, our arguments are mainly based on the existence of minimal 
strong foliations and the existence of blender-horseshoes. We also prove 
that any non-hyperbolic ergodic measure is in the intersection of the 
convex hulls of the measures with positive central exponent and with 
negative central exponent.
This talk is based on joint work with L.J.Díaz, M.Rams, and B.Santiago.

Friday, 30 November 2018 (9:30 - 12:00)

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.

Everyone is welcome to attend

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

For to be free is not merely to cast off one's chains, but to live in a way
that respects and enhances the freedom of others. Nelson Mandela