5 papers · 1 filter
Kolmogorov invariant torus theorem for weakly interacting particles I: Full dimensional tori
Dmitry Dolgopyat, Bassam Fayad, Jaime Paradela
We develop an abstract KAM theorem for systems of infinitely many interacting particles with decaying masses and all-to-all interactions. Using this framework, we construct full-di…
Robustly transitive behavior in symplectic dynamics
Jaime Paradela
We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we…
Partially hyperbolic dynamics in the 3-body problem
Marcel Guardia, Jaime Paradela
We construct symplectic blenders for two classical Hamiltonian systems: the 3-body problem and its restricted version. We use these objects to show that both models exhibit a robus…
A degenerate Arnold diffusion mechanism in the Restricted 3 Body Problem
Marcel Guardia, Jaime Paradela, Tere M. Seara
A major question in dynamical systems is to understand the mechanisms driving global instability in the 3 Body Problem (3BP), which models the motion of three bodies under Newtonia…
Parabolic saddles and Newhouse domains in Celestial Mechanics
Miguel Garrido, Pau MartÃn, Jaime Paradela
In the 70s McGehee introduced a compactification of the phase space of the restricted 3-body problem by gluing a manifold of periodic orbits "at infinity". Although from the dynami…