Abstract:
A.A. Andronov most intensive and fruitful activities as a scientist, educator, and organizer unfolded in the city Nizhny Novgorod (then it was Gorky). In 1931–1932, a group of talented young scientists (A.A. Andronov, M.T. Grekhova, V.I. Gaponov, E.A. Leontovich, and A.G. Lyubina) moved there permanently, followed by G.S. Gorelik in 1938. A.A. Andronov viewed the establishment of major scientific centers in the provinces as a vital state task. Our talk outlines one of the school's research areas related to so-called rough dynamical systems the key developmental stages. The concept of "roughness" for differential equations systems on a plane, introduced by A.A. Andronov and L.S. Pontryagin in 1937, received a significant impetus for development in the 1960s and 70s. This period in the dynamical systems theory is known as the "hyperbolic revolution," during which the term "roughness" was largely superseded by the now more popular term "structural stability." The presentation will provide an overview of results, including those by the author, demonstrating the current state of the theory of hyperbolic dynamical systems.
The lecture duration is 90 minutes.
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