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Mathematics

D-Index
40
Citations
6537
World Ranking
2062
National Ranking
876

Overview

Rafael de la Llave is affiliated with the Georgia Institute of Technology in the United States. Their research spans the fields of Physics and Astronomy as well as Mathematics, with notable contributions in several subfields including Statistical and Nonlinear Physics, Mathematical Physics, Astronomy and Astrophysics, Numerical Analysis, and Aerospace Engineering.

The principal topics covered in de la Llave's work include Quantum chaos and dynamical systems, Mathematical Dynamics and Fractals, Astro and Planetary Science, Numerical methods for differential equations, Spacecraft Dynamics and Control, Nonlinear Dynamics and Pattern Formation, and Scientific Research and Discoveries.

De la Llave has published extensively, with recent papers reflecting a focus on dynamics in celestial mechanics and nonlinear systems. Selected recent works are:

  • Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems (2022, Celestial Mechanics and Dynamical Astronomy)
  • KAM quasi-periodic tori for the dissipative spin-orbit problem (2022, Cineca Institutional Research Information System, Tor Vergata University)
  • Parameterization method for state-dependent delay perturbation of an ordinary differential equation (2020, arXiv, Cornell University)
  • High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem (2021, Communications in Nonlinear Science and Numerical Simulation)
  • Response Solutions to Quasi-Periodically Forced Systems, Even to Possibly Ill-Posed PDEs, with Strong Dissipation and any Frequency Vectors (2020, SIAM Journal on Mathematical Analysis)

Frequent coauthors in their research include Joan Gimeno, Renato Calleja, Alessandra Celletti, Bhanu Kumar, and Rodney L. Anderson. Collaborative efforts have contributed to a range of studies primarily in nonlinear dynamics and celestial mechanics.

De la Llave's publications appear often in certain venues, highlighting their preferred platforms for dissemination. These include:

  • arXiv (Cornell University) with 21 publications
  • Communications in Nonlinear Science and Numerical Simulation with 3 publications
  • Nonlinearity with 3 publications
  • SIAM Journal on Applied Dynamical Systems with 3 publications
  • Celestial Mechanics and Dynamical Astronomy with 2 publications

Best Publications

  • The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces

    Xavier Cabre;Ernest Fontich;Rafael De La Llave

  • The parameterization method for invariant manifolds III: overview and applications

    Xavier Cabré;Ernest Fontich;Rafael de la Llave

  • The parameterization method for invariant manifolds II: regularity with respect to parameters

    Xavier Cabre;Ernest Fontich;Rafael De La Llave

  • Canonical perturbation theory of Anosov systems, and regularity results for the Livsic cohomology equation

    Unknown

  • Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation

    Unknown

  • A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the Large Gap Problem: Heuristics And Rigorous Verification on a Model

    Amadeu Delshams;Rafael de la Llave;Tere M. Seara

  • Relativistic Stability of Matter - I

    Charles L. Fefferman;Rafael de la Llave

  • A Geometric Approach to the Existence of Orbits with Unbounded Energy in Generic Periodic Perturbations by a Potential of Generic Geodesic Flows of ? 2}

    Amadeu Delshams;Rafael de la Llave;Tere M. Seara

  • A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi-Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity

    Unknown

  • GEOMETRIC PROPERTIES OF THE SCATTERING MAP OF A NORMALLY HYPERBOLIC INVARIANT MANIFOLD

    Amadeu Delshams;Rafael de la Llave;Tere M. Seara

  • A parameterization method for the computation of invariant tori andtheir whiskers in quasi-periodic maps: Numerical algorithms

    Àlex Haro;Rafael de la Llave

  • A KAM theory for conformally symplectic systems: Efficient algorithms and their validation

    Renato C. Calleja;Alessandra Celletti;Rafael de la Llave

  • KAM theory and a partial justification of Greene's criterion for nontwist maps

    Amadeu Delshams;Rafael de la Llave

  • Planelike minimizers in periodic media

    Luis A. Caffarelli;Rafael de la Llave

  • Regularity of the composition operator in spaces of Hölder functions

    Rafael De La Llave;R. Obaya

  • Invariants for smooth conjugacy of hyperbolic dynamical systems II

    Unknown

  • Computation of limit cycles and their isochrons: Fast algorithms and their convergence

    Gemma Huguet;Rafael de la Llave

  • A rigorous partial justification of Greene's criterion

    Corrado Falcolini;Rafael de la Llave

  • A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification

    Renato Calleja;Rafael de la Llave

  • On Squirt Singularities in Hydrodynamics

    Diego Córdoba;Charles Louis Fefferman;Rafael De La Llave

  • On Irwin’s proof of the pseudostable manifold theorem

    Rafael de la Llave;C. Eugene Wayne

  • TOPOLOGICAL METHODS IN THE INSTABILITY PROBLEM OF HAMILTONIAN SYSTEMS

    Marian Gidea;Rafael De La Llave

  • Construction of invariant whiskered tori by a parameterization method. Part I: Maps and flows in finite dimensions

    Ernest Fontich;Rafael de la Llave;Yannick Sire

  • Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows

    Amadeu Delshams;Rafael de la Llave;Tere M. Seara

  • Smooth Ergodic Theory and Its Applications

    Anatole Katok;Rafael de la Llave;Yakov Pesin;Howard Weiss

Frequent Co-Authors

Enrico Valdinoci
Enrico Valdinoci University of Western Australia
Xavier Cabré
Xavier Cabré Universitat Politècnica de Catalunya
Luis A. Caffarelli
Luis A. Caffarelli The University of Texas at Austin
C. Eugene Wayne
C. Eugene Wayne Boston University
Ioannis G. Kevrekidis
Ioannis G. Kevrekidis Johns Hopkins University
Charles Fefferman
Charles Fefferman Princeton University
Linda R. Petzold
Linda R. Petzold University of California, Santa Barbara
Anatole Katok
Anatole Katok Pennsylvania State University
Carles Simó
Carles Simó University of Barcelona
Wassim M. Haddad
Wassim M. Haddad Georgia Institute of Technology

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