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
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 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.
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.
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.
Geometrical Methods in the Theory of Ordinary Differential Equations
Vladimir Igorevich Arnold.
Singularities of Differentiable Maps, Volume 2: Monodromy and Asymptotics of Integrals
S.M. Gusein-Zade;A.N. Varchenko;Alexander N. Varchenko;V.I. Arnold.
Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
Annales de l'Institut Fourier (1966)
Singularities of Differentiable Maps
V. I. Arnold;S. M. Gusein-Zade;A. N. Varchenko.
Topological methods in hydrodynamics
Vladimir I. Arnold;Boris A. Khesin.
SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
Vladimir I Arnol'd.
Russian Mathematical Surveys (1963)
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)
Ordinary Differential Equations
Fred Brauer;Vladimir I. Arnol'd;Roger Cook.
Dynamical Systems III
Vladimir I. Arnold.
If you think any of the details on this page are incorrect, let us know.
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: