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## Weak* convergence of operator means

Izvestiya. Mathematics. 2011. Vol. 75. No. 6. P. 1165-1183.

Romanov A., Ergodic Theory and Dynamical Systems 2016 Vol. 36 No. 1 P. 198-214

For a continuous semicascade on a metrizable compact set Ω, we consider the weak* convergence of generalized operator ergodic means in EndC*(Ω). We discuss conditions on the dynamical system under which: every ergodic net contains a convergent sequence; all ergodic nets converge; all ergodic sequences converge. We study the relationships between the convergence of ergodic means and ...

Added: August 21, 2014

Romanov A., Известия РАН. Серия математическая 2011 Т. 75 № 6 С. 79-98

Для линейного сжатия U в пространстве Банаха X обсуждаются условия сходимости соответствующих его сопряженному оператору U* эргодических операторных сетей в W*O-топологии пространства End X*. Точки накопления всевозможных таких сетей образуют выпуклое компактное множество L в End X*, представляющее собой ядро полугруппы операторов G - замкнутой выпуклой оболочки степеней U*. Показано, что все эргодические сети слабо* ...

Added: October 10, 2012

Romanov A., Ergodic Properties of Discrete Dynamical Systems and Enveloping Semigroups / Cornell University. Series math "arxiv.org". 2013. No. 1309.6283.

For a continuous semicascade on a metrizable compact set Ω, we consider the weak* convergence of generalized operator ergodic means in End C*(Ω). We discuss conditions on the dynamical system under which: (a) every ergodic net contains a convergent subsequence; (b) all ergodic nets converge; (c) all ergodic sequences converge. We study the relationships between ...

Added: November 19, 2013

A.V. Romanov, Ergodic Properties of tame dynamical systems / Cornell University. Series math "arxiv.org". 2018. No. 1806.09132.

We study the problem on the weak-star decomposability of a topological N0-dynamical system (Ω, '), where ' is an endomorphism of a metric compact set Ω, into ergodic components in terms of the associated enveloping semigroups. In the tame case (where the Ellis semigroup E(Ω,') consists of B1-transformations Ω → Ω), we show that (i) ...

Added: July 3, 2018

Зелик С. В., Chepyzhov V. V., Доклады Академии наук 2014 Т. 455 № 5 С. 512-517

We study regular global attractors of the dynamical systems corresponding to dissipative evolution equations and their nonautonomous perturbations. We prove that the nonautonomous dynamical system (process) resulting from a small nonautonomous perturbation of an autonomous dynamical system (semigroup) having a regular attractor has a regular nonautonomous attractor as well. Moreover, the symmetric Hausdorff deviation of ...

Added: August 26, 2014

Romanov A., Functional Analysis and Its Applications 2013 Vol. 47 No. 2 P. 160-163

A relationship is considered between ergodic properties of a discrete dynamical system on a compact metric space Ω and characteristics of companion algebro-topological objects, namely, the Ellis enveloping semigroup E, the Kohler enveloping operator semigroup Γ, and the semigroup G being the closure of the convex hull of Γ in the weak-star topology on the ...

Added: November 18, 2013

Shilin I., Доклады Академии наук 2016 Т. 469 № 3 С. 287-290

В работе показано, что неустойчивость аттракторов Милнора по Ляпунову является локально топологически типичным динамическим явлением, которое наблюдается в присутствии устойчивых гомоклинических касаний для 2-сжимающих периодических седел. ...

Added: October 14, 2018

Protasov V., Systems and Control Letters 2016 Vol. 90 P. 54-60

We prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slower than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon ...

Added: February 22, 2016

Kleptsyn V., Alvarez S., Malicet D. et al., Groups with infinitely many ends acting analytically on the circle / Cornell University. Series math "arxiv.org". 2015.

Added: June 22, 2016

Blokh A., Oversteegen L., Ptacek R. et al., The parameter space of cubic laminations with a fixed critical leaf / Cornell University. Series math "arxiv.org". 2015.

Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we consider slices of the family of cubic invariant laminations defined by a fixed critical leaf with non-periodic endpoints. We parameterize each slice by ...

Added: February 11, 2015

Pardalos P. M., Rassias T. undefined., Springer, 2014

This volume consists of chapters written by eminent scientists and engineers from the international community and presents significant advances in several theories, and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, and Discrete Mathematics and Geometry, as well as several ...

Added: May 30, 2014

Stankevich N., Kazakov A., Gonchenko S., Chaos 2020 Vol. 30 Article 123129

The generalized four-dimensional Rössler system is studied. Main bifurcation scenarios leading to a hyperchaos are described phenomenologically and their implementation in the model is demonstrated. In particular, we show that the formation of hyperchaotic invariant sets is related mainly to cascades (finite or infinite) of nondegenerate bifurcations of two types: period-doubling bifurcations of saddle cycles with a ...

Added: January 18, 2021

Stanislav Minkov, Ivan Shilin, Attractors of direct products / Cornell University. Series math "arxiv.org". 2020. No. arXiv:2011.04824.

For Milnor, statistical, and minimal attractors, we construct examples of smooth flows φ on S^2 for which the attractor of the Cartesian square of φ is smaller than the Cartesian square of the attractor of φ. In the example for the minimal attractors, the flow φ also has an SRB-measure such that its square does ...

Added: November 12, 2020

Stankevich N., Shchegoleva N. A., Sataev I. R. et al., Journal of Computational and Nonlinear Dynamics 2020 Vol. 15 No. 11 P. 111001

Using an example a system of two coupled generators of quasiperiodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involve saddle tori occurring at their ...

Added: September 4, 2020

Springer, 2009

Vladimir Arnold is 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 first volume of his Collected Works focuses on representations of functions, celestial mechanics, and ...

Added: February 20, 2013

Blokh A., Oversteegen L., Ptacek R. et al., Smart criticality / Cornell University. Series math "arxiv.org". 2014.

A crucial fact established by Thurston in his 1985 preprint is that distinct \emph{minors} of quadratic laminations do not cross inside the unit disk; this led to his construction of a combinatorial model of the Mandelbrot set. Thurston's argument is based upon the fact that \emph{majors} of a quadratic lamination never enter the region between ...

Added: February 11, 2015

Romanov A., Функциональный анализ и его приложения 2013 Т. 47 № 2 С. 92-96

Рассматриваются связи эргодических свойств дискретной динамической системы на метрическом компакте Ω с характеристиками сопутствующих ей алгебро-топологических объектов: обволакивающей полугруппы Эллиса E, операторной обволакивающей полугруппы Кёлер Г, а также полугруппы G, представляющей собой замыкание выпуклой оболочки множества Г в слабой топологии пространства операторов End C*(Ω). Основные результаты формулируются для ординарных (обладающих метризуемой полугруппой E) полукаскадов и ...

Added: September 1, 2014

Pardalos P. M., Rassias T. undefined., Springer, 2014

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional ...

Added: May 30, 2014

V.L. Chernyshev, Tolchennikov A. A., Russian Journal of Mathematical Physics 2017 Vol. 24 No. 3 P. 290-298

In the problem of determining the asymptotics for the number of points moving along a metric tree, a polynomial approximation that uses Barnes’ multiple Bernoulli polynomials is found. The connection between the second term of the asymptotic expansion and the graph structure is discussed. ...

Added: October 3, 2017

Романов А. В., Mathematical Notes, USA 2019 Vol. 106 No. 2 P. 286-295

The problem of the ∗-weak decomposability into ergodic components of a topological N0-dynamical system (Ω, ϕ), where ϕ is a continuous endomorphism of a compact metric space Ω, is considered in terms of the associated enveloping semigroups. It is shown that, in the tame case (where the Ellis semigroup E(Ω, ϕ) consists of endomorphisms of ...

Added: September 9, 2019

Smilga I., Harmonic functions on the Sierpinski triangle / Cornell University. Series arXiv "math". 2012. No. 1205.4442.

In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle - more precisely, of their restriction to a side of the triangle. First we present a general formula that gives the Hölder exponent of such a function in a given point. From this formula, we deduce ...

Added: September 26, 2018

Aranson S. K., Belitsky G. R., Zhuzhoma E. V., American Mathematical Society, 1996

The book is an introduction to the qualitative theory of dynamical systems on manifolds of low dimension (on the circle and on surfaces). Along with classical results, it reflects the most significant achevements in this area obtained in recent times. The reader of this book need to be familiar only with basic courses in differential ...

Added: October 2, 2014

Filimonov D., Клепцын В. А., Nonlinearity 2014 Vol. 27 No. 6 P. 1205-1223

We study possible one-end finitely presented subgroups of <img />, acting without finite orbits. Our main result, theorem 1, establishes that any such action possesses the so-called property (<img />), that allows one to make distortion-controlled expansion and is thus sufficient to conclude that the action is Lebesgue-ergodic. We also propose a path towards full ...

Added: October 23, 2014

Romaskevich O. L., L'Enseignement Mathématique 2014

We consider 3 -periodic orbits in an elliptic billiard. Numerical experiments conducted by Dan Reznik have shown that the locus of the centers of inscribed circles of the corresponding triangles is an ellipse. We prove this fact by the complexification of the problem coupled with the complex law of reflection. ...

Added: December 25, 2014