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| Name |
Title |
Date |
Time |
Room |
| Irene De Blasi (University of Turin) | Billiards with potentials in Celestial Mechanics: refractive caseAbstract: A new type of billiard system, of interest for Celestial Mechanics, is taken into consideration: here, a closed refraction interface separates two regions in which different potentials (harmonic and Keplerian) act. The result is a variation of the classical Birkhoff billiard where the particle enters and exits from the domain, and can be used, for example, to mimic the motion of a particle in an elliptic galaxy having a central mass.
This model, which can be studied both in two and three dimensions, presents strong analogies with the more studied Kepler billiard, where a Keplerian inner potential is associated with a reflecting wall.
The dynamical properties of the system can be studied by adapting techniques coming from billiards’ theory, variational methods and results for general area-preserving maps, and regard principally the existence and stability properties of equilibrium trajectories or the arising of chaotic behaviours.
Work in collaboration with V. Barutello and S. Terracini.
References:
De Blasi I., Terracini S., Refraction periodic trajectories in central mass galaxies. Nonlinear Analysis (2022)
De Blasi I., Terracini, S., On some refraction billiards. Discrete and Continuous Dynamical Systems (2022)
Barutello V.L., De Blasi I., Terracini, S., Chaotic dynamics in refraction galactic billiards. Nonlinearity (2023)
Barutello V.L., De Blasi I., A note on chaotic billiards with potentials, Preprint (2023) |
Tuesday, 23 April 2024 |
13:00 |
HXLY 410 |
| Raphael Krikorian (Université de Cergy-Pontoise) | Abstract: |
Tuesday, 30 April 2024 |
13:00 |
Huxley 140 |
| Peter Giesl (University of Sussex) | Abstract: |
Tuesday, 7 May 2024 |
13:00 |
Huxley 140 |
| Emmanuel Fleurentin (UNC Chapel Hill) | Investigating Most Probable Escape Paths over Periodic Boundaries: a Dynamical Systems ApproachAbstract: Noise-induced tipping (N-tipping) emerges when random fluctuations prompt transitions from one (meta)stable state to another, potentially as a rare event. In this talk, we delineate new techniques for determining Most Probable Escapes Paths (MPEPs) in stochastic differential equations over periodic boundaries. We utilize a dynamical system approach to unravel MPEPs for the intermediate noise regime. We discuss the framework for computing the MPEPs by first looking at intersections of stable and unstable manifolds of invariant sets of a Hamiltonian system derived from the Euler-Lagrange equations of the Freidlin-Wentzell (FW) functional. The Maslov index helps identify which critical points of the FW functional are local minimizers and assists in explaining the effects of the interaction of noise and the deterministic flow. The Onsager-Machlup functional, which is treated as a perturbation of the FW functional, will provide a selection mechanism to pick out the MPEP. We will illustrate our approach and compare our theoretical prediction with Monte Carlo simulations in the Inverted Van der Pol system and a carbon cycle model. |
Tuesday, 18 June 2024 |
13:00 |
Huxley 140 |
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