4 papers
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…