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Omega-Limit Sets of Generic Points of Partially Hyperbolic Diffeomorphisms
Functional Analysis and Its Applications. 2016. Vol. 50. No. 1. P. 48–53.
Minkov S. S., Окунев А. В.
We prove that, for any E u ⊕ E cs partially hyperbolic C 2 diffeomorphism, the ω-limit set of a generic (with respect to the Lebesgue measure) point is a union of unstable leaves. As a corollary, we prove a conjecture made by Ilyashenko in his 2011 paper that the Milnor attractor is a union of unstable leaves. In the paper mentioned above, Ilyashenko reduced the local generecity of the existence of a “thick” Milnor attractor in the class of boundary-preserving diffeomorphisms of the product of the interval and the 2-torus to this conjecture.
S. V. Zelik, Russian Mathematical Surveys 2023 Vol. 78 No. 4 P. 635–777
Добавлено: 21 января 2024 г.
Добавлено: 20 декабря 2023 г.
L. M. Lerman, K. N. Trifonov, Journal of Geometry and Physics 2024 Vol. 195 No. 2 Article 105038
Добавлено: 31 октября 2023 г.
Sheshmani A., Long C., Vafa C. и др., Communications in Mathematical Physics 2023 Vol. 399 No. 3 P. 1991–2043
Добавлено: 29 августа 2023 г.
Гринес В. З., Минц Д. И., Regular and Chaotic Dynamics 2023 Vol. 28 No. 3 P. 295–308
Добавлено: 2 августа 2023 г.
Доказывается существование глобального аттрактора регуляризированной системы Эйлера–Бардины с диссипацией на двумерной сфере и в произвольных областях на сфере. Получены явные оценки фрактальной размерности аттрактора в терминах физических параметров ...
Добавлено: 9 мая 2023 г.
Seržant I., Мороз Г. А., Humanities and Social Sciences Communications 2022 Vol. 9 Article 58
Добавлено: 23 января 2022 г.
Springer Nature Switzerland AG, 2019.
Добавлено: 29 октября 2021 г.
Stanislav Minkov, Шилин И. С., Qualitative Theory of Dynamical Systems 2021 Vol. 20 No. 3 Article 77
Добавлено: 16 сентября 2021 г.
Stanislav Minkov, Ivan Shilin, / Series math "arxiv.org". 2020. No. arXiv:2011.04824.
Добавлено: 12 ноября 2020 г.
Bekmaganbetov K., Chechkin G., Чепыжов В. В. и др., Discrete and Continuous Dynamical Systems 2017 Vol. 37 No. 5 P. 2375–2393
We consider the 3D Navier--Stokes systems with randomly rapidly oscillating right--hand sides. Under the assumption that the random functions are ergodic and statistically homogeneous in space variables or in time variables we prove that the trajectory attractors of these systems tend to the trajectory attractors of homogenized 3D Navier--Stokes systems whose right--hand sides are the ...
Добавлено: 7 июня 2017 г.
Волк Д. С., Liverani C., De Simoi J. и др., Journal of Statistical Physics 2016
Добавлено: 11 октября 2016 г.
Волк Д. С., Discrete and Continuous Dynamical Systems 2014 Vol. 34 No. 5 P. 2307–2314
Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In this paper, we prove the finiteness conjecture for the ITMs of three intervals. Namely, the subset of ITMs of finite ...
Добавлено: 30 декабря 2015 г.
Волк Д. С., Kleptsyn V., Moscow Mathematical Journal 2014 Vol. 14 No. 2 P. 339–365
A one-dimensional confined nonlinear random walk is a tuple of N diffeomorphisms of the unit interval driven by a probabilistic Markov chain. For generic such walks, we obtain a geometric characterization of their ergodic stationary measures and prove that all of them have negative Lyapunov exponents. These measures appear to be probabilistic manifestations of physical measures for ...
Добавлено: 30 декабря 2015 г.
Волк Д. С., Ergodic Theory and Dynamical Systems 2014 Vol. 34 No. 2 P. 693–704
Добавлено: 28 декабря 2015 г.
Волк Д. С., Kleptsyn V., Nonlinearity 2014 Vol. 27 No. 7 P. 1595–1601
Добавлено: 22 декабря 2015 г.
Починка О. В., Levchenko Y., Гринес В. З. и др., Regular and Chaotic Dynamics 2014 Vol. 19 No. 4 P. 506–512
Добавлено: 11 сентября 2014 г.
Ильяшенко Ю. С., Шилин И. С., Proceedings of the Steklov Institute of Mathematics 2012 Vol. 277 No. 1 P. 84–93
There are different non-equivalent definitions of attractors in the theory of dynamical systems. The most common are two definitions: the maximal attractor and the Milnor attractor. The maximal attractor is by definition Lyapunov stable, but it is often in some ways excessive. The definition of Milnor attractor is more realistic from the physical point of ...
Добавлено: 5 февраля 2013 г.