Dynamical Systems at ICTP

Statistical stability of interval maps with critical points and singularities, by Jose F. Alves, Dalmi Gama, Stefano Luzzatto.

We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy some expansivity and bounded recurrence conditions. This generalizes known results for maps with critical points and bounded derivatives and in particular proves statistical stability of Lorenz-like maps with critical points and singularities studied in [S. Luzzatto and W. Tucker. Non-uniformly expanding dynamics in maps with singularities and criticalities. Inst. Hautes Etudes Sci. Publ. Math., (89):179-226, 1999]. We introduce a natural metric on the space of maps with discontinuities which does not seem to have been used in the literature before.

Statistical stability of interval maps with critical points and singularities We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy some expansivity and bounded recurrence conditions. This gene...

Congratulations to David Ruelle who, together with Joel Lebowitz and Elliot Lieb, has been awarded the prestigious ICTP Dirac Medal for 2022.

ICTP - 2022 ICTP Dirac Medal Winners Announced ICTP has awarded its 2022 Dirac Medal to three distinguished physicists "for groundbreaking and mathematically rigorous contributions to the understanding of the statistical mechanics of classical and quantum physical systems".

ICTP M A T H E M A T I C S S E M I N A R S 2022

Thursday 7 July, at 16:00 hrs CEST
Speaker: Damien Thomine (Université Paris-Sud)
Title: Probabilistic potential theory for dynamical systems

Abstract: Probabilistic potential theory relates Markov chains and harmonic functions. It offers the tools to compute, for instance, the probability that a random walk hits a specified target before another; or, thinking in terms of open systems, that the walk leaves the space at a specified point.

We adapt those results to dynamical systems. Our aim is to estimate, in a spatially periodic hyperbolic system, the probability of hitting a specified target before another. This work involves tools from potential theory (specifically, a balayage identity), transfer operators with spectral degeneracies, and perturbative arguments.

This will be a hybrid seminar. All are very welcome to join either online or in person.
Venue: Luigi Stasi Lecture Room (ICTP Leonardo Da Vinci Building), for those wishing to attend in person.
Register in advance for this meeting:

https://zoom.us/meeting/register/tJIlc-ysqDooHNBsuerJh6gHICViOSjgR8YL

After registering, you will receive a confirmation email containing information about joining the meeting.

Welcome! You are invited to join a meeting: Probabilistic potential theory for dynamical systems. After registering, you will receive a confirmation email about joining the meeting. Abstract: Probabilistic potential theory relates Markov chains and harmonic functions. It offers the tools to compute, for instance, the probability that a random walk hits a specified target before another; or, thinking in terms of open systems, that the walk leaves the space at a specified point.....