Dia: Dimecres 14 d'octubre de 2026

Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.

• Hora: 16h00m

  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 C_bif(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: Tue Oct 13 11:07:02 2026