- Home
- Best Scientists - Mathematics
- Rafael de la Llave

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
31
Citations
4,050
189
World Ranking
2596
National Ranking
1085

- Quantum mechanics
- Mathematical analysis
- Geometry

Invariant, Mathematical analysis, Pure mathematics, Integrable system and Symplectic geometry are his primary areas of study. The Invariant study combines topics in areas such as Discrete mathematics, Manifold, Simple and Torus. His work on Periodic orbits as part of general Mathematical analysis study is frequently connected to Normally hyperbolic invariant manifold, therefore bridging the gap between diverse disciplines of science and establishing a new relationship between them.

His work in the fields of Invariant manifold, Minimal surface and Covering space overlaps with other areas such as Mean curvature. Rafael de la Llave works mostly in the field of Integrable system, limiting it down to topics relating to Hamiltonian system and, in certain cases, Jet. Rafael de la Llave has included themes like Applied mathematics and Sobolev space in his Symplectic geometry study.

- The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces (170 citations)
- The parameterization method for invariant manifolds III: overview and applications (131 citations)
- A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the Large Gap Problem: Heuristics And Rigorous Verification on a Model (121 citations)

His main research concerns Mathematical analysis, Pure mathematics, Kolmogorov–Arnold–Moser theorem, Invariant and Torus. The study incorporates disciplines such as Perturbation and Invariant in addition to Mathematical analysis. His work on Manifold, Stable manifold and Diffeomorphism as part of his general Pure mathematics study is frequently connected to Foliation, thereby bridging the divide between different branches of science.

His work deals with themes such as Differentiable function, Mathematical proof, Diophantine equation and Applied mathematics, which intersect with Kolmogorov–Arnold–Moser theorem. His research in Invariant intersects with topics in Dynamical systems theory, Invariant manifold and Linear subspace. His Torus research is multidisciplinary, incorporating perspectives in Symplectic geometry and Lattice.

- Mathematical analysis (48.11%)
- Pure mathematics (27.57%)
- Kolmogorov–Arnold–Moser theorem (23.78%)

- Pure mathematics (27.57%)
- Applied mathematics (11.89%)
- Mathematical analysis (48.11%)

Rafael de la Llave focuses on Pure mathematics, Applied mathematics, Mathematical analysis, Symplectic geometry and Kolmogorov–Arnold–Moser theorem. His Pure mathematics study integrates concerns from other disciplines, such as Torus and Metric. Rafael de la Llave combines subjects such as Lyapunov function, Eigenvalues and eigenvectors, Perturbation and Three-body problem with his study of Mathematical analysis.

His Symplectic geometry research incorporates themes from Embedding, Diophantine equation, Dissipative system and Tangent space. His work carried out in the field of Kolmogorov–Arnold–Moser theorem brings together such families of science as Fixed point, Contraction mapping, Monodromy, Differentiable function and Degenerate energy levels. He regularly links together related areas like Manifold in his Invariant studies.

- An A Posteriori KAM Theorem for Whiskered Tori in Hamiltonian Partial Differential Equations with Applications to some Ill-Posed Equations (13 citations)
- Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations (6 citations)
- A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results (5 citations)

- Quantum mechanics
- Mathematical analysis
- Topology

Rafael de la Llave spends much of his time researching Mathematical analysis, Well-posed problem, Normally hyperbolic invariant manifold, Hamiltonian system and Applied mathematics. His research combines Torus and Mathematical analysis. His research integrates issues of Gevrey class and Newton's method in his study of Torus.

In his research on the topic of Gevrey class, Nonlinear system, Invariant, Stable manifold and Manifold is strongly related with Bounded function. His Well-posed problem study combines topics from a wide range of disciplines, such as Partial differential equation and Integral equation. Rafael de la Llave interconnects Delay differential equation, Series expansion, Uniqueness, Power series and Series in the investigation of issues within Applied mathematics.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

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

Xavier Cabre;Ernest Fontich;Rafael De La Llave.

Indiana University Mathematics Journal **(2003)**

279 Citations

The parameterization method for invariant manifolds III: overview and applications

Xavier Cabré;Ernest Fontich;Rafael de la Llave.

Journal of Differential Equations **(2005)**

266 Citations

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

Xavier Cabre;Ernest Fontich;Rafael De La Llave.

Indiana University Mathematics Journal **(2003)**

191 Citations

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.

**(2005)**

186 Citations

Relativistic Stability of Matter - I

Charles L. Fefferman;Rafael de la Llave.

Revista Matematica Iberoamericana **(1986)**

175 Citations

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.

Communications in Mathematical Physics **(2000)**

134 Citations

Planelike minimizers in periodic media

Luis A. Caffarelli;Rafael de la Llave.

Communications on Pure and Applied Mathematics **(2001)**

116 Citations

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

Amadeu Delshams;Rafael de la Llave.

Siam Journal on Mathematical Analysis **(2000)**

110 Citations

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

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

Advances in Mathematics **(2008)**

109 Citations

Regularity of the composition operator in spaces of Hölder functions

Rafael De La Llave;R. Obaya.

Discrete and Continuous Dynamical Systems **(1998)**

108 Citations

If you think any of the details on this page are incorrect, let us know.

Contact us

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

University of Western Australia

Universitat Politècnica de Catalunya

The University of Texas at Austin

Princeton University

Johns Hopkins University

Georgia Institute of Technology

University of Barcelona

University of California, Santa Barbara

City College of New York

Pennsylvania State University

Queen Mary University of London

York University

Lawrence Livermore National Laboratory

National University of Singapore

Mid Sweden University

California Institute of Technology

Georgia Institute of Technology

Astellas Pharma (Japan)

Rutgers, The State University of New Jersey

University of California, San Diego

University of Wuppertal

Indiana University

University of Manitoba

RMIT University

Leipzig University

Tel Aviv University

Something went wrong. Please try again later.