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ВИДЕОТЕКА |
Конференция «Hyperbolic Dynamics and Structural Stability», посвященная 85-летию Д. В. Аносова
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From Skew Products to Geometrically Integrable Maps in the Plane L. S. Efremova Lobachevski State University of Nizhni Novgorod |
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Аннотация: The structure of the space of The concept of geometrically integrable self-maps of the compact plane sets is introduced. Criteria of the geometric integrability are proved and examples of these maps are considered [E2]. Comparison of geometrically integrable maps and skew products properties is given. The problem of the coexistence of periodic points periods of geometrically integrable maps is solved [E2], [EM]. The concept of a generalized Lorenz self-map of a compact plane set is introduced. The set of generalized Lorenz maps contains the proper subset of "two-dimensional" Lorenz maps that arise in the standard geometric Lorenz model [ABSh]. Solution of the problem of the coexistence of periodic points periods of generalized Lorenz maps is presented [E2]. [E1] L.S. Efremova, Dynamics of skew products of interval maps, Russian Math. Surv., 72:1 (2017), 101–178. [E2] L.S. Efremova, Geometrically integrable maps in the plane and their periodic orbits, Lobachevskii Journ. Math, 42:10 (2021), 2315–2324. [EM] L.S. Efremova, E.N. Makhrova One-dimensional dynamical systems, Russ. Math. Surv., 76:5 (2021), 81–146. [ABSh] V.S. Afraimovich, V.V. Bykov, L.P. Shilnikov, Attractive nonrough limit sets of Lorenz-attractor type, Trudy Moskovskogo Matematich. Obshchestva, 44 (1982), 150–212. Язык доклада: английский |