What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- 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)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Mathematical analysis (48.11%)
- Pure mathematics (27.57%)
- Kolmogorov–Arnold–Moser theorem (23.78%)
What were the highlights of his more recent work (between 2017-2021)?
- Pure mathematics (27.57%)
- Applied mathematics (11.89%)
- Mathematical analysis (48.11%)
In recent papers he was focusing on the following fields of study:
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.
Between 2017 and 2021, his most popular works were:
- 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)
In his most recent research, the most cited papers focused on:
- 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.
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