1 citations · 1 across the 5 of their papers we have counts for
5 papers
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…