Dia: Dimecres, 14 de setembre de 2022
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
També ONLINE https://meet.google.com/zvg-pajn-owr
A càrrec de: Jaume Paradela (UPC)
Títol: Unstable Motions in the Restricted Planar Elliptic Three Body Problem
Resum: Consider the restricted planar elliptic 3 body problem (RPE3BP), where a massless body moves on the gravitational field generated by two bodies, called primaries, which have masses μ∈(0,1/2] and 1-μ and revolve one around each other in Keplerian ellipses of eccentricity ε∈(0,1). We prove that the RPE3BP exhibits unstable dynamics: for any value μ∈ (0,1/2), we build orbits along which the angular momentum G of the massless body experiences an arbitrarily large variation provided the eccentricity of the primaries is small enough. This kind of unstable motion is also referred to as Arnold diffusion in the literature.
The proof relies on the existence of a transition chain of heteroclinic orbits to a Topological Normally Hyperbolic Invariant Cylinder (TNHIC). Two main sets of tools are developed to construct this diffusive mechanism in the RPE3BP. First, for the study of highly anisotropic splitting (involving exponentially and non exponentially small directions) between the invariant manifolds of pairs of partially hyperbolic invariant tori. Second, for the analysis of two distinct scattering maps associated to two different transversal intersections of the invariant manifolds of a (Topological) NHIC. In particular, for comparing them when they are exponentially close to each other. This is a joint work with Marcel Guardia and Tere Seara.
Last updated: Tuesday, 27-Sep-2022 10:19:51 CEST