Speaker: Vered Rom-Kedar (Weizmann Institute of Science)
Time: 2025-09-29 14:00
Zoom Meeting ID: 844 0594 7424 (Passcode:076895)
Abstract:
The dynamics associated with mechanical Hamiltonian systems with smooth potentials that include sharp fronts is traditionally modeled by Hamiltonian impact systems: a class of generalized billiards by which the dynamics in the domain’s interior are governed by smooth potentials and at the domain’s boundaries by elastic reflections. I will first discuss the properties of this singular limit, culminating in the 2024 work with D. Turaev in which we established the non-ergodicity of smooth N repelling particles in a box at arbitrarily high energy. Then, I will introduce the class of quasi-integrable Hamiltonian impact systems, where the motion on some level sets is conjugated to a directed motion on a translation surface of a genus larger than one. We propose mechanical realizations of such systems, analyze ergodic properties and quantum properties of classes of such systems, and study their behavior under perturbations. In particular, we show that these give rise to families of discontinuous, piecewise smooth area preserving maps, and we study some of the properties of such maps. Based on joint works with, in chronological order, D. Turaev, L. Lerman, M. Kloc, M. Pnueli, L. Becker, S. Elliott, B. Firester, S. Gonen Cohen, K. Fraczek, O. Yaniv, I. Pazi and A. Zobova.
About Speaker:
Professor Rom-Kedar is a researcher working at the Weizmann Institute of Science. She is an expert on Chaotic Dynamics, Hamiltonian Dynamics, and their applications to Science, Medicine, and Engineering.
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