14 citations · 21 across the 9 of their papers we have counts for
9 papers
On the density of Lyapunov unstable elliptic equilibria
Bassam Fayad, Jaime Paradela, Maria Saprykina +1
We prove that any real-analytic Hamiltonian in five or more degrees-of-freedom, with a locally integrable non-degenerate elliptic equilibrium with indefinite quadratic part, can be…
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…
Parabolic saddles and Newhouse domains in Celestial Mechanics
Miguel Garrido, Pau Martín, 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…
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…
Oscillatory Motions in the Restricted 3-body Problem: A functional analytic approach
Jaime Paradela, Susanna Terracini
A fundamental question in Celestial Mechanics is to analyze the possible final motions of the Restricted -body Problem, that is, to provide the qualitative description of its co…
Hyperbolic dynamics and oscillatory motions in the 3 Body Problem
Marcel Guardia, Pau Martín, Jaime Paradela +1
Consider the planar 3 Body Problem with masses . In this paper we address two fundamental questions: the existence of oscillatory motions and of chaotic hyperbolic s…
Symbolic Dynamics in the Elliptic Isosceles Restricted Three Body Problem
Marcel Guardia, Jaime Paradela, Tere-M. Seara +1
The elliptic isosceles restricted three body problem (REI3BP) models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodi…