12 citations · 36 across the 15 of their papers we have counts for
15 papers
Families of relative periodic orbits in the planar three-body problem via consecutive alignments
Joan Gimeno, Marc Jorba-Cuscó, Begoña Nicolás
Relative periodic orbits (RPOs) are solutions of the three-body problem that are periodic in a uniformly rotating reference frame and, in general, quasi-periodic in inertial coordi…
Numerical Computation of Quasiperiodic Reducible Saddle-Node Bifurcations: a Parameterization Method Approach
Jordi-Lluís Figueras, Joan Gimeno, Jeremy P. Parker
We present a method for computing reducible, normally hyperbolic, invariant tori with internal quasiperiodic dynamics in autonomous ordinary differential equation systems. The appr…
Effective Stability of Near-Rectilinear Halo Orbits in the Earth-Moon System
Joan Gimeno, Luke T. Peterson
Near-rectilinear halo orbits (NRHOs) around Earth-Moon L2 in the Circular Restricted 3-Body Problem (CR3BP) exhibit a complex dynamical landscape, featuring a band of normally elli…
Lag-Induced Critical Transitions to Extinction in Replicating Systems
Edward A. Turner, Francisco Crespo, Joan Gimeno +3
Replicating systems sustained by error-prone enzymatic amplification can undergo critical transitions between persistence and extinction. In RNA viruses, such transitions are class…
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…
Numerical computation of high-order expansions of invariant manifolds of high-dimensional tori
Joan Gimeno, Àngel Jorba, Begoña Nicolás +1
In this paper we present a procedure to compute reducible invariant tori and their stable and unstable manifolds in stroboscopic Poincaré maps. The method has two steps. In the fir…
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…
Deep Non-Crossing Quantiles through the Partial Derivative
Axel Brando, Joan Gimeno, Jose A. Rodríguez-Serrano +1
Quantile Regression (QR) provides a way to approximate a single conditional quantile. To have a more informative description of the conditional distribution, QR can be merged with…
Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs
Joan Gimeno, Jean-Philippe Lessard, J. D. Mireles James +1
A computer-assisted argument is given, which provides existence proofs for periodic orbits in state-dependent delayed perturbations of ordinary differential equations (ODEs). Assum…
The spin-spin problem in Celestial Mechanics
Alessandra Celletti, Joan Gimeno, Mauricio Misquero
We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual gravitational influence. We assume that the spin axis of each ellipsoid coincides with its shortes…
KAM quasi-periodic tori for the dissipative spin-orbit problem
Renato Calleja, Alessandra Celletti, Joan Gimeno +1
We provide evidence of the existence of KAM quasi-periodic attractors for a dissipative model in Celestial Mechanics. We compute the attractors extremely close to the breakdown thr…
Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction
Renato Calleja, Alessandra Celletti, Joan Gimeno +1
We consider the dissipative spin-orbit problem in Celestial Mechanics, which describes the rotational motion of a triaxial satellite moving on a Keplerian orbit subject to tidal fo…
Persistence and Smooth Dependence on Parameters of Periodic Orbits in Functional Differential Equations Close to an ODE or an Evolutionary PDE
Jiaqi Yang, Joan Gimeno, Rafael de la Llave
We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or…
Numerical computation of periodic orbits and isochrons for state-dependent delay perturbation of an ODE in the plane
Joan Gimeno, Jiaqi Yang, Rafael de la Llave
We present algorithms and their implementation to compute limit cycles and their isochrons for state-dependent delay equations (SDDE's) which are perturbed from a planar differenti…
Parameterization method for state-dependent delay perturbation of an ordinary differential equation
Jiaqi Yang, Joan Gimeno, Rafael de la Llave
We consider state-dependent delay equations (SDDE) obtained by adding delays to a planar ordinary differential equation with a limit cycle. These situations appear in models of sev…