10 citations · 19 across the 8 of their papers we have counts for
9 papers
The existence of solutions for nonlinear elliptic equations: Simple proofs and extensions of a paper by Y. Shi
Xiaodan Xu, Rafael de la Llave, Fenfen Wang
The paper [Shi19] uses the Craig-Wayne-Bourgain method to construct solutions of an elliptic problem involving parameters. The results of [Shi19] include regularity assumptions on…
Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation
Rafael de la Llave, Maria Saprykina
Consider an analytic Hamiltonian system near its analytic invariant torus carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at $\ma…
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…
Gevrey estimates for asymptotic expansions of tori in weakly dissipative systems
Adrian P. Bustamante, Rafael de la Llave
We consider a singular perturbation for a family of analytic symplectic maps of the annulus possessing a KAM torus. The perturbation introduces dissipation and contains an adjustab…
Expansions in the delay of quasi-periodic solutions for state dependent delay equations
Alfonso Casal, Livia Corsi, Rafael de la Llave
We consider several models of State Dependent Delay Differential Equations (SDDEs), in which the delay is affected by a small parameter. This is a very singular perturbation since…
Global effect of non-conservative perturbations on homoclinic orbits
Marian Gidea, Rafael de la Llave, Maxwell Musser
We study the effect of time-dependent, non-conservative perturbations on the dynamics along homoclinic orbits to a normally hyperbolic invariant manifold. We assume that the unpert…
Existence of whiskered KAM tori of conformally symplectic systems
Renato C. Calleja, Alessandra Celletti, Rafael de la Llave
We study the existence of whiskered tori in a family of conformally symplectic maps depending on parameters . Whiskered tori are tori on which the motion is a rotation, bu…
Domains of analyticity of Lindstedt expansions of KAM tori in dissipative perturbations of Hamiltonian systems
Renato C. Calleja, Alessandra Celletti, Rafael de la Llave
Many problems in Physics are described by dynamical systems that are conformally symplectic (e.g., mechanical systems with a friction proportional to the velocity, variational prob…
Boundaries of Siegel disks - numerical studies of their dynamics and regularity
Rafael de la Llave, Nikola P. Petrov
Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates whic…