1 citations · 2 across the 9 of their papers we have counts for
9 papers
Geometric, topological and dynamical properties of conformally symplectic systems, normally hyperbolic invariant manifolds, and scattering maps
Marian Gidea, Rafael de la Llave, Tere M-Seara
Conformally symplectic diffeomorphisms transform a symplectic form on a manifold M into a multiple of itself, . We assume is bounded, as some…
Persistence of hyperbolic solutions of ODE's under functional perturbations: Applications to the motion of relativistic charged particles
Joan Gimeno, Rafael de la Llave, Jiaqi Yang
We rigorously construct a variety of orbits for certain delay differential equations, including the electrodynamic equations formulated by Wheeler and Feynman in 1949. These equati…
KAM Theory for almost-periodic equilibria in one dimensional almost-periodic media
Yujia An, Rafael de la Llave, Xifeng Su +2
We consider one dimensional chains of interacting particles subjected to one dimensional almost-periodic media. We formulate and prove two KAM type theorems corresponding to both s…
Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
Renato Calleja, Alessandra Celletti, Joan Gimeno +1
We consider a Celestial Mechanics model: the spin-orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper i…
Nonconmutative coboundary equations over integrable systems
Rafael de la Llave, Maria Saprykina
\def\G{\mathcal G} \def\M{\mathcal M} \def\cE{\mathcal E} We prove an analog of Livšic theorem for real-analytic families of cocycles over an integrable system with values in a Ban…
Resonances and Phase Locking Phenomena for Foliation Preserving Torus Maps
Xiaolong He, Rafael de la Llave
It is well known for experts that resonances in nonlinear systems lead to new invariant objects that lead to new behaviors. The goal of this paper is to study the invariant sets ge…
Computing the Invariant Circle and the Foliation by Stable Manifolds for a 2-D Map by the Parameterization Method: Numerical Implementation and Results
Yian Yao, Rafael De La Llave
We present and implement an algorithm for computing the invariant circle and the corresponding stable manifolds for 2-dimensional maps. The algorithm is based on the parameterizati…
Computing the Invariant Circle and its Stable Manifolds for a 2-D Map by the Parameterization Method: Effective Algorithms and Rigorous Proofs of Convergence
Yian Yao, Rafael De La Llave
We present and analyze rigorously a quadratically convergent algorithm to compute an invariant circle for 2-dimensional maps along with the corresponding foliation by stable manifo…
Computation and Analysis of Jupiter-Europa and Jupiter-Ganymede Resonant Orbits in the Planar Concentric Circular Restricted 4-Body Problem
Bhanu Kumar, Rodney L. Anderson, Rafael de la Llave +1
Many unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equations of motion. In th…