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- Vladimir I. Arnold

Mathematics

Russia

2023

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
55
Citations
49,821
288
World Ranking
550
National Ranking
6

2023 - Research.com Mathematics in Russia Leader Award

2022 - Research.com Mathematics in Russia Leader Award

2001 - Wolf Prize in Mathematics for his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory.

2001 - Dannie Heineman Prize for Mathematical Physics, American Physical Society and American Institute of Physics

1983 - Member of the National Academy of Sciences

- 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.

- 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)

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.

- Pure mathematics (25.56%)
- Mathematical analysis (26.40%)
- Gravitational singularity (16.29%)

- Pure mathematics (25.56%)
- Combinatorics (11.52%)
- Gravitational singularity (16.29%)

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.

- Arnold's Problems (169 citations)
- Singularities of Differentiable Maps, Volume 1 (83 citations)
- Lectures on Partial Differential Equations (52 citations)

- 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.

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.

Mathematical Methods of Classical Mechanics

Vladimir Igorevič Arnol'd.

**(1974)**

22625 Citations

Geometrical Methods in the Theory of Ordinary Differential Equations

Vladimir Igorevich Arnold.

**(1983)**

4165 Citations

Singularities of Differentiable Maps, Volume 2: Monodromy and Asymptotics of Integrals

S.M. Gusein-Zade;A.N. Varchenko;Alexander N. Varchenko;V.I. Arnold.

**(1988)**

2693 Citations

Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits

Vladimir Arnold.

Annales de l'Institut Fourier **(1966)**

2470 Citations

Singularities of Differentiable Maps

V. I. Arnold;S. M. Gusein-Zade;A. N. Varchenko.

**(1985)**

1965 Citations

Topological methods in hydrodynamics

Vladimir I. Arnold;Boris A. Khesin.

**(1998)**

1537 Citations

SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS

Vladimir I Arnol'd.

Russian Mathematical Surveys **(1963)**

1463 Citations

PROOF OF A THEOREM OF A.?N.?KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

V I Arnol'd.

Russian Mathematical Surveys **(1963)**

1129 Citations

Ordinary Differential Equations

Fred Brauer;Vladimir I. Arnol'd;Roger Cook.

**(1973)**

1042 Citations

Dynamical Systems III

Vladimir I. Arnold.

**(1987)**

623 Citations

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