22 citations · 50 across the 17 of their papers we have counts for
23 papers
High-Order Resonant Orbit Manifold Expansions For Mission Design In the Planar Circular Restricted 3-Body Problem
Bhanu Kumar, Rodney L. Anderson, Rafael de la Llave
In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for design…
KAM theory for some dissipative systems
Renato Calleja, Alessandra Celletti, Rafael de la Llave
Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial sa…
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…
KAM estimates for the dissipative standard map
Renato Calleja, Alessandra Celletti, Rafael de la Llave
From the beginning of KAM theory, it was realized that its applicability to realistic problems depended on developing quantitative estimates on the sizes of the perturbations allow…
Response solutions to quasi-periodically forced systems, even to possibly ill-posed PDEs, with strong dissipation and any frequency vectors
Fenfen Wang, Rafael de la Llave
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very s…
Whiskered KAM Tori of Conformally Symplectic Systems
Renato C. Calleja, Alessandra Celletti, Rafael de la Llave
We investigate the existence of whiskered tori in some dissipative systems, called \sl conformally symplectic \rm systems, having the property that they transform the symplectic fo…