Starts 28 Nov 2018 14:00
Ends 28 Nov 2018 16:30
Central European Time
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Two-day workshop on Dynamical Systems (Wednesday, 28th November 2018)
ICTP
Leonardo Building - Luigi Stasi Seminar Room
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.
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.