What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Quantum mechanics
- Geometry
His primary areas of study are Pure mathematics, Mathematical analysis, Classical mechanics, Gravitational singularity and Dynamical systems theory.
His work on Lemma as part of general Pure mathematics research is frequently linked to Bifurcation diagram, bridging the gap between disciplines.
While the research belongs to areas of Mathematical analysis, Vladimir I. Arnold spends his time largely on the problem of Hamiltonian, intersecting his research to questions surrounding Quasi periodic, Mathematical proof, Integrable system, Adiabatic invariant and Fundamental lemma.
His Classical mechanics research includes themes of Hamiltonian mechanics and Perturbation theory.
His study looks at the intersection of Hamiltonian mechanics and topics like Formalism with Equations of motion.
His research in Gravitational singularity intersects with topics in Legendre polynomials, Critical point, Differentiable function, Symplectic geometry and Degenerate energy levels.
His most cited work include:
- Mathematical Methods of Classical Mechanics (6950 citations)
- Geometrical Methods in the Theory of Ordinary Differential Equations (2502 citations)
- Mathematical methods of classical mechanics (2155 citations)
What are the main themes of his work throughout his whole career to date?
His main research concerns Pure mathematics, Mathematical analysis, Gravitational singularity, Classical mechanics and Combinatorics.
His study in Monodromy, Holomorphic function, Morse theory, Manifold and Symplectic manifold falls under the purview of Pure mathematics.
His work deals with themes such as Vector field and Surface, which intersect with Mathematical analysis.
He interconnects Singularity, Boundary, Catastrophe theory and Mathematical physics in the investigation of issues within Gravitational singularity.
As part of his studies on Classical mechanics, Vladimir I. Arnold frequently links adjacent subjects like Dynamical systems theory.
Vladimir I. Arnold combines topics linked to Discrete mathematics with his work on Combinatorics.
He most often published in these fields:
- Pure mathematics (25.56%)
- Mathematical analysis (26.40%)
- Gravitational singularity (16.29%)
What were the highlights of his more recent work (between 2006-2021)?
- Pure mathematics (25.56%)
- Combinatorics (11.52%)
- Gravitational singularity (16.29%)
In recent papers he was focusing on the following fields of study:
Vladimir I. Arnold focuses on Pure mathematics, Combinatorics, Gravitational singularity, Mathematical analysis and Discrete mathematics.
His Pure mathematics research incorporates elements of Singularity and Taylor series.
His work carried out in the field of Gravitational singularity brings together such families of science as Intersection, Differentiable function and Boundary.
Vladimir I. Arnold performs integrative study on Mathematical analysis and Bifurcation diagram.
As a part of the same scientific study, Vladimir I. Arnold usually deals with the Discrete mathematics, concentrating on Algebra over a field and frequently concerns with Semigroup, Topology and Geometry.
His study in Morse theory is interdisciplinary in nature, drawing from both Manifold and Topological classification.
Between 2006 and 2021, his most popular works were:
- Arnold's Problems (169 citations)
- Singularities of Differentiable Maps, Volume 1 (83 citations)
- Lectures on Partial Differential Equations (52 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Quantum mechanics
- Geometry
Vladimir I. Arnold spends much of his time researching Discrete mathematics, Gravitational singularity, Real number, Pure mathematics and Classical mechanics.
His work in Discrete mathematics covers topics such as Algebra over a field which are related to areas like Integer, Extension, Regular polygon and Topology.
His Gravitational singularity study incorporates themes from Differentiable function, Directional derivative and Catastrophe theory.
His study with Differentiable function involves better knowledge in Mathematical analysis.
His study brings together the fields of Ellipsoid and Pure mathematics.
His studies examine the connections between Classical mechanics and genetics, as well as such issues in Integral geometry, with regards to Laplace operator.
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