31 citations · 163 across the 23 of their papers we have counts for
27 papers
Existence and Regularity of Stable Resonant Spectral Submanifolds and Linearization Maps
Florian Kogelbauer, Rafael de la Llave
We prove the existence of -regular sub-stable invariant manifolds and conjugacies for analytic maps near a fixed point in the presence of resonances, assuming an inver…
4th Body-Induced Secondary Resonance Overlapping Inside Unstable Resonant Orbit Families: a Jupiter-Ganymede 4:3 + Europa Case Study
Bhanu Kumar, Rodney L. Anderson, Rafael de la Llave
The overlapping of mean-motion resonances is useful for low or zero-propellant space mission design, but while most related prior work uses a planar CRTBP model, tours of multi-moo…
A simple proof of Gevrey estimates for expansions of quasi-periodic orbits: dissipative models and lower dimensional tori
Adrián P. Bustamante, Rafael de la Llave
We consider standard-like/Froeschlé maps with a dissipation and nonlinear perturbation. That is \[ T_\varepsilon(p,q) = \left( (1 - γ\varepsilon^3) p + μ+ \varepsilon V'(q), q + (1…
Rapid GPU-Assisted Search and Parameterization-Based Refinement and Continuation of Connections between Tori in Periodically Perturbed Planar Circular Restricted 3-Body Problems
Bhanu Kumar, Rodney L. Anderson, Rafael de la Llave
When the planar circular restricted 3-body problem (PCRTBP) is periodically perturbed, as occurs in many useful astrodynamics models, most unstable periodic orbits persist as whisk…
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…
Rapid and Accurate Methods for Computing Whiskered Tori and their Manifolds in Periodically Perturbed Planar Circular Restricted 3-Body Problems
Bhanu Kumar, Rodney L. Anderson, Rafael de la Llave
When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families of unstable periodic orbits break up into whiskered tori, with most tori persisting in…
Melnikov method for non-conservative perturbations of the three-body problem
Marian Gidea, Rafael de la Llave, Maxwell Musser
We consider the planar circular restricted three-body problem (PCRTBP), as a model for the motion of a spacecraft relative to the Earth-Moon system. We focus on the Lagrange equili…
Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems
Qinbo Chen, Rafael de la Llave
The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the following a priori unstable Hamiltonian system with a ti…
Lyapunov exponents everywhere and rigidity
Fernando Micena, Rafael de la Llave
In the present work we obtain rigidity results analysing the set of regular points, in the sense of Oseledec's Theorem. It is presented a study on the possibility of an Anosov diff…
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…
Global Melnikov Theory in Hamiltonian Systems with General Time-dependent Perturbations
Marian Gidea, Rafael de la Llave
We consider a mechanical system consisting of penduli and a -dimensional generalized rotator subject to a time-dependent perturbation. The perturbation is not assumed to be…
On the Global Dynamics of an Electroencephalographic Mean Field Model of the Neocortex
Farshad Shirani, Wassim M. Haddad, Rafael de la Llave
This paper investigates the global dynamics of a mean field model of the electroencephalogram developed by Liley et al., 2002. The model is presented as a system of coupled ordinar…
Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification
Maciej J. Capinski, Marian Gidea, Rafael de la Llave
We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits genera…
Resonant equilibrium configurations in quasi-periodic media: KAM theory
Rafael de la Llave, Xifeng Su, Lei Zhang
We develop an a-posteriori KAM theory for the equilibrium equations for quasi-periodic solutions in a quasi-periodic Frenkel-Kontorova model when the frequency of the solutions res…
Resonant Equilibrium configurations in quasi-periodic media: perturbative expansions
Rafael de la Llave, Xifeng Su, Lei Zhang
We consider 1-D quasi-periodic Frenkel-Kontorova models. We study the existence of equilibria whose frequency (i.e. the inverse of the density of deposited material) is resonant wi…
Response solutions for quasi-periodically forced, dissipative wave equations
Renato C. Calleja, Alessandra Celletti, Livia Corsi +1
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not…
Barriers to Transport and Mixing in Volume-Preserving Maps with Nonzero Flux
Adam M Fox, Rafael de la Llave
In this paper we identify the geometric structures that restrict transport and mixing in perturbations of integrable volume-preserving systems with nonzero net flux. Unlike KAM tor…
Construction of invariant whiskered tori by a parameterization method. Part II: Quasi-periodic and almost periodic breathers in coupled map lattices
Ernest Fontich, Rafael de la Llave, Yannick Sire
We construct quasi-periodic and almost periodic solutions for coupled Hamiltonian systems on an infinite lattice which is translation invariant. The couplings can be long range, pr…
Localized Stable Manifolds for Whiskered Tori in Coupled Map Lattices with Decaying Interaction
Daniel Blazevski, Rafael de la Llave
In this paper we consider lattice systems coupled by local interactions. We prove invariant manifold theorems for whiskered tori (we recall that whiskered tori are quasi-periodic s…
Perturbations of geodesic flows by recurrent dynamics
Marian Gidea, Rafael de la Llave
We consider a geodesic flow on a compact manifold endowed with a Riemannian (or Finsler, or Lorentz) metric satisfying some generic, explicit conditions. We couple the geodesic flo…
Instability of high dimensional Hamiltonian Systems: Multiple resonances do not impede diffusion
Amadeu Delshams, Rafael de la Llave, Tere M. Seara
We consider models given by Hamiltonians of the form where are d-dimensional ac…
Invariant manifolds for analytic difference equations
Rafael de la Llave, Hector E. Lomeli
We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and…
Perturbation and Numerical Methods for Computing the Minimal Average Energy
Timothy Blass, Rafael de la Llave
We investigate the differentiability of minimal average energy associated to the functionals $S_\ep (u) = \int_{\mathbb{R}^d} (1/2)|\nabla u|^2 + \ep V(x,u)\, dx$, using numerical…