Dia: Dimecres 16 de setembre de 2026
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Begoña Nicolás (Universidad de Santiago de Compostela)
Títol: Relative Periodic Orbits in the Three-Body Problem from consecutive alignments
Resum: Relative periodic orbits (RPOs) are a fundamental class of solutions of the planar Three-Body Problem (TBP) that are periodic in a uniformly rotating frame and, in general, quasi-periodic in inertial coordinates. Their study dates back to Poincaré, who in his 1892 Méthodes Nouvelles described solutions characterized by recurrent syzygies and corresponding velocity symmetries.
In this work, we develop a numerical procedure that exploits two consecutive alignments to compute and continue one-parameter families of RPOs in the planar Newtonian TBP. We obtain Poincaré, Hill, and binary-type families, revealing transitions between nearly circular and highly eccentric motion, stability changes near resonances and turning points, and absolute periodic orbits for rational rotation angles.
These families not only provide coherent three-body motions that can be used to determine stable configurations for three prescribed masses, but also serve as natural building blocks for time-periodic restricted four-body models, with potential applications to a wide range of astronomical systems.
This is a joint work with J. Gimeno, À. Jorba and M. Jorba-Cuscó. See https://arxiv.org/abs/2609.01585
A càrrec de: Vassili Gelfreich (University of Warwick)
Títol: Embedded Solitons, Homoclinic Orbits and the Stokes Phenomenon
Resum: We investigate solitons in a generalized Korteweg–de Vries equation. After a travelling-wave reduction, the problem becomes one of finding homoclinic orbits to a saddle–centre equilibrium in a singularly perturbed reversible Hamiltonian system. Such homoclinic orbits are not structurally stable and are generally destroyed by arbitrarily small perturbations. The presence of additional parameters, however, allows them to persist as a codimension-one phenomenon. In the singular limit, this persistence is governed by the vanishing of a parameter-dependent Stokes constant associated with an inner equation.
This talk is based on joint work with R. Barrio, A. R. Champneys, J. T. Lázaro, and J. R. Pacha.
Last updated: Fri Sep 25 11:30:43 2026