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## Non-uniform Kozlov-Treschev averagings in the ergodic theorem

. 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.

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

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

Anikin A. Y., Brüning J., Dobrokhotov S. et al., Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 265-276

In this paper, we consider the spectral problem for the magnetic Schrödinger operator on the 2-D plane (x1, x2) with the constant magnetic field normal to this plane and with the potential V having the form of a harmonic oscillator in the direction x1 and periodic with respect to variable x2. Such a potential can ...

Added: September 18, 2019

Shirokov D., Advances in Applied Clifford Algebras 2017 Vol. 27 No. 1 P. 149-163

In this paper we consider different operators acting on Clifford algebras. We consider Reynolds operator of Salingaros’ vee group. This operator “average” an action of Salingaros’ vee group on Clifford algebra. We consider conjugate action on Clifford algebra. We present a relation between these operators and projection operators onto fixed subspaces of Clifford algebras. Using ...

Added: September 27, 2016

V. G. Danilov, R. K. Gaydukov, Russian Journal of Mathematical Physics 2022 Vol. 29 No. 4 P. 431-455

A problem of a nonstationary incompressible viscous fluid ow along a plate with small fast-oscillating irregularities on the surface for a large Reynolds number is considered by using rigorous methods of mathematical physics. Depending on the scales of irregularities in the problem under study, there arises a solution that describes the double-deck or triple-deck structure boundary layers on ...

Added: August 19, 2020

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

Springer, 2013

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry. ...

Added: February 20, 2013

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

Volk D., Liverani C., De Simoi J. et al., Journal of Statistical Physics 2016

We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Freidlin-Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a "sink" with all the ...

Added: October 11, 2016

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

Blank M., [б.и.], 2017

We study typical points with respect to ergofic averaging of a general dynamical system. ...

Added: February 10, 2018

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

M.V.Karasev, E.M.Novikova, Russian Journal of Mathematical Physics 2015 Vol. 22 No. 4 P. 463-468

We study dynamics of a charge in the planar Penning trap in which the direction of magnetic ﬁeld does not coincide with the trap axis. Under some combined resonance condition on the deviation angle and magnitudes of magnetic and electric ﬁelds, the trajectories of a charge are near-periodic. We describe the reduction to a top-like ...

Added: October 22, 2015

Danilov V., European Journal of Mechanics - B/Fluids 2019 Vol. 74 P. 152-158

A stratified liquid with two layers separated by a fast oscillating interface in the case of Raleigh--Taylor instability
is considered. The averaged equations are derived, and it is shown that a mushy region of a certain density appears after averaging. The similarity between this fact and the case of unstable jump decay is discussed. ...

Added: October 21, 2018

Gaydukov R., Сибирский журнал вычислительной математики 2022 Т. 15 № 2 С. 97-109

A viscous liquid flow along a semi-infinite plate with small periodic irregularities on the surface was
considered for large Reynolds numbers. The flow near the plate is described by Prandtl equations with
induced pressure which are non-classical PDE, because they contain a limiting term. The main goal is to
construct a numerical algorithm for solving these equations with ...

Added: June 10, 2020

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

Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148

In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...

Added: May 17, 2017

Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600

We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...

Added: October 25, 2018

Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188

The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...

Added: December 2, 2019

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...

Added: March 13, 2016