Person: Anosov, Dmitrii Viktorovich
Dmitri Anosov was a Russian mathematician who worked in dynamical systems theory.
Mathematical Profile (Excerpt):
- Dmitrii Viktorovich showed his abilities while at high school, entering the Physics Moscow Olympiad and the Mathematics Moscow Olympiad on several occasions.
- His work was supervised by Pontryagin and during this period Anosov published a number of papers including: On stability of equilibrium states of relay systems (Russian) (1959); Averaging in systems of ordinary differential equations with rapidly oscillating solutions (Russian) (1960); and Limit cycles of systems of differential equations with small parameters in the highest derivatives (Russian) (1960).
- Anosov defended his thesis on averaging in systems of ordinary differential equations at Moscow University in 1961.
- An event happened in 1961 which changed the direction of Anosov's research.
- At the same time, Smale met with a group of young Soviet mathematicians, among them Dmitrii Anosov, a student of Pontryagin, and mentioned some difficult unsolved problems, in particular, the problem of structural stability of hyperbolic automorphisms of a torus and geodesic flows on closed manifolds of negative curvature.
- It should be noted that Anosov was already the author of several papers, of which one, on averaging in multi-frequency systems, is still highly regarded today.
- Nevertheless, he easily switched his interests to Smale's problems, and in a year he had solved them as particular cases in his investigation of the U-systems he introduced, now called Anosov systems.
- Smale's discovery and its development by Anosov marked the beginning of the 'hyperbolic revolution' in mathematics.
- Anosov discovered a fundamental fact concerning the ergodic theory of smooth dynamical systems, namely the absolute continuity of transversal foliations.
- In 1968 Anosov became a professor in the Department of Mechanics and Mathematics at Moscow State University where he taught for the rest of his career.
- In the 1970s Anosov published papers such as Existence of smooth ergodic flows on smooth manifolds (Russian) (1974) and was an invited speaker at the International Congress of Mathematicians at Vancouver in 1974 when he gave the lecture Geodesics and Finsler geometry.
- In addition to his work on the analysis of manifolds, Anosov has written many historical and biographical articles.
- Anosov has received many honours for his achievements.
Born 30 November 1936, Moscow, Russia. Died 7 August 2014, Moscow, Russia.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive