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The 8th International Conference on Differential and Functional Differential Equations.
2017.
We study typical points with respect to ergofic averaging of a general dynamical system.
Blank M., Nonlinearity 2017 Vol. 30 No. 12 P. 4649-4664
The classical Birkhoff ergodic theorem in its most popular version says that the
time average along a single typical trajectory of a dynamical system is equal
to the space average with respect to the ergodic invariant distribution. This
result is one of the cornerstones of the entire ergodic theory and its numerous
applications. Two questions related to this subject ...
Added: July 16, 2018
Bizyaev I. A., Borisov A., Mamaev I., Regular and Chaotic Dynamics 2016 Vol. 21 No. 1 P. 136-146
This paper is concerned with the motion of the Chaplygin sleigh on the surface of a circular cylinder. In the case of inertial motion, the problem reduces to the study of the dynamical system on a (two-dimensional) torus and to the classification of singular points. Particular cases in which the system admits an invariant measure ...
Added: April 5, 2017
Bizyaev I. A., Borisov A., Mamaev I., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2016 Vol. 12 P. 1-19
In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess a nonmaximal rank, and in the general case an invariant measure and Casimir functions can be globally absent for them. ...
Added: April 5, 2017
Bogachev V., Veretennikov A., Shaposhnikov S., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2015 Т. 460 № 5 С. 507-511
Методами уравнений в частных производных установлены достаточные условия дифференцируемости инвариантных мер диффузионных процессов по параметру ...
Added: October 11, 2015
Cherkashin Danila, Kryzhevich S., Topological Methods in Nonlinear Analysis 2017 Vol. 50 No. 1 P. 125-150
We consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomorphisms such that any pseudotrajectory can be shadowed by a finite number of ...
Added: January 31, 2018
Bizyaev I. A., Борисов А. В., Мамаев И. С., Труды Математического института им. В.А. Стеклова РАН 2016 Т. 294 С. 268-292
This paper is concerned with the nonholonomic Suslov problem and its generalization proposed by Chaplygin. The issue of the existence of an invariant measure with singular density (having singularities at some points of phase space) is discussed. ...
Added: April 4, 2017
V'yugin V., Theory of Computing Systems 2016 P. 403-423
We study a stability property of probability laws with respect to small violations of algorithmic randomness. Some sufficient
condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like the
strong law of large numbers, the law of iterated logarithm, and even Birkhoff's pointwise ergodic theorem for ergodic
transformations, are stable in ...
Added: May 16, 2015
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2015 Т. 432 С. 224-260
The paper generalizes the results by E. Janvresse, T. de la Rue and Y. Velenik [18] on fluctuations in ergodic sums for the Pascal adic transformation in the case of Lebesgue measure for a wide class of functions. In particular, we answer several questions from [18]. ...
Added: March 15, 2015
Gurevicha B. M., S.A. Komech, Tempelman A. A., Moscow Mathematical Journal 2019 Vol. 19 No. 1 P. 77-88
For some symbolic dynamical systems we study the value of the boundary deformation for a small ball in the phase space during a period of time depending on the center and radius of the ball. For actions of countable Abelian groups, a version of the Mean Ergodic theorem with averaging over random sets is proved ...
Added: December 17, 2020
Minabutdinov A., Лодкин А. А., Манаев И. Е., / Санкт-Петербургское математическое общество. Серия MSP "Preprints of the St. Petersburg Mathematical Society". 2014. № 11.
The paper generalizes the results by \'E. Janvresse, T. de la Rue and Y. Velenik [22] and the work [9] of the third author on fluctuations in ergodic sums for the Pascal adic in the case of arbitrary ergodic invariant measures. In particular, we answer several questions from [22] and [9]. ...
Added: March 28, 2015
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2016 Т. 448 С. 177-200
We prove existence of limiting curves (describing deviations in ergodic theorem) for cylindrical functions for Polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function we give necessary condition of a limiting curve to exist. Our work generalizes results by E'. Janvresse, T. de la Rue and Y. Velenik. ...
Added: October 14, 2016
Minabutdinov A., Лодкин А. А., Записки научных семинаров ПОМИ РАН 2015 Т. 437 С. 145-183
The paper generalizes the results by E. Janvresse, T. de la Rue and Y. Velenik on fluctuations in ergodic sums for the Pascal adic transformation in the case of any ergodic invariant measure and cylindric function. The result on non-discreteness of the spectrum of the Pascal adic is stated. ...
Added: October 14, 2015
Blank M., Moscow Mathematical Journal 2019 Vol. 19 No. 1 P. 37-50
Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent points. We show that under some mild technical assumptions the set of non-recurrent points is of zero reference measure. Necessary and ...
Added: October 8, 2019
Klimenko A. V., Буфетов А. И., Сириес К., Успехи математических наук 2020
В заметке представлен результат о сходимости почти всюду сферических средних для сохраняющщих вероятностную меру действий фуксовой группы, если группа и набор образующих удовлетворяют условию "ровных углов" (even corners). Именно, группа обладает фундаментальной областью, для которой граница замощения диска её образами состоит из целых геодезических, а в качестве набора образующих взяты элементы группы, переводящие эту фундаментальную ...
Added: October 31, 2019
Bogachev V., 2020 Vol. 75 No. 3 P. 393-425
Generalizations and refnements are given for results of Kozlov and Treschev on non-uniform averagings in the ergodic theorem in the case of operator semigroups on spaces of integrable functions and semigroups of
measure-preserving transformations. Conditions on the averaging measures are studied under which the averages converge for broad classes of integrable functions. ...
Added: October 23, 2020
Skripchenko A., Hubert P., Avila A., / Cornell University. Series math "arxiv.org". 2014. No. 1412.7913.
We study chaotic plane sections of some particular family of triply periodic surfaces. The question about possible behavior of such sections was posed by S. P. Novikov. We prove some estimations on diffusion rate of these sections using the connection between Novikov's problem and systems of isometries - some natural generalization of interval exchange transformations. ...
Added: January 27, 2015
Blank M., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2015 Т. 461 № 2 С. 1-5
We study the functional properties of the concept of interlacing introduced by I.M. Gelfand and show that in the context of collective random walks, this property leads to synchronization. ...
Added: March 20, 2015
Blank M., Advances in Mathematics 2022 Vol. 406 Article 108529
We study measure-theoretical aspects of torus piecewise isometries.
Not much is known about this type of dynamical systems, except for
the special case of one-dimensional interval exchange mappings. The
last case is fundamentally different from the general situation
in the presence of an invariant measure (Lebesgue measure), which
helps a lot in the analysis. Due to the absence of good ...
Added: June 26, 2022
Blank M., Доклады Академии наук 2013 Т. 448 № 6 С. 629-632
We give conditions for unique ergodicity for a discrete time collective
random walk on a continuous circle. Individual particles in this collective
motion perform independent (and different) random walks conditioned
by the assumption that the particles cannot overrun each other.
Deterministic version of this system is studied as well. ...
Added: November 25, 2014
Klimenko A. V., Bufetov A., Series C., / Cornell University. Series math "arxiv.org". 2018. No. 1805.11743.
Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving ...
Added: September 18, 2018
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013