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.
Dia: Dimecres 30 de setembre de 2026
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Marcel Guàrdia (Universitat de Barcelona)
Títol: Partially hyperbolic dynamics in the 3-body problem
Resum: In this talk I will explain how to construct symplectic blenders for two classical Hamiltonian systems: the 3-body problem and its restricted version. These objects lead to a strong form of topological instability.
This is a joint work with Jaime Paradela.
Dia: Dimecres 14 d'octubre de 2026
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Alexandra Lillo (UPC)
Títol: Dynamics of families of n-ECOs in the Elliptic Restricted Three-Body Problem.
Resum: We study n-ejection-collision orbits (n-ECOs) in the Elliptic Restricted Three-Body Problem (ERTBP): trajectories that eject from a primary and collide with it again after n ≥ 1 finite excursions. In the circular problem (CRTBP), it is known that for any mass parameter μ and any n there exist exactly four families of n-ECOs for sufficiently large values of the Jacobi constant C. We explore how this picture changes in the ERTBP, a non-autonomous, 2π-periodic perturbation of the CRTBP depending on the eccentricity e and the initial true anomaly f0. Using Levi-Civita regularization and the inherent symmetry of the problem, we compute the initial conditions of n-ECOs over a wide range of parameters. We show numerically that the four-family structure persists for sufficiently large initial values C0 of the Jacobi Constant, in agreement with the known analytical results (small e and μ, n=1) and well beyond that regime. Below a critical value Cbif(e, f0) the families bifurcate; we compute this surface numerically and describe its main features, including jumps in e and oscillations in f0.
Last updated: Thu Oct 29 15:28:46 2026