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## Anosov Actions of Isometry Groups on Lorentzian 2-Orbifolds

Lobachevskii Journal of Mathematics. 2021. Vol. 42. No. 14. P. 3324-3335.

Bogolepova E., Zhukova N.

We prove a criterion of an Anosov action of the isometry group for compact Lorentzian 2-orbifolds. It is proved also that a non-compact complete flat Lorentzian 2-orbifold has an Anosov isometry if and only if its isometry group Lie acts improperly. The existence of chaotic behavior of such Anosov actions is investigated. It is shown that among smooth 2-orbifolds other than manifolds, only the “pillow” and the Z_2-cone admit the specified Lorentz metric with an Anosov action of the isometry group. The corresponding Lorentzian metrics and groups of isometries are

indicated.

Боголепова Е. В., Lobachevskii Journal of Mathematics 2022

We prove a criterion of an Anosov action of the isometry group for compact Lorentzian $2$-orbifolds.
It is proved also that a non-compact complete flat Lorentzian $2$-orbifold has an Anosov isometry if and only if its
isometry group Lie acts improperly. The existence of chaotic behavior of such Anosov actions is investigated.
It is shown that among smooth ...

Added: November 17, 2021

Боголепова Е. В., Zhukova N., Известия высших учебных заведений. Поволжский регион. Физико-математические науки 2019 № 1 С. 14-28

Using the bundle of pseudo-orthogonal frames some canonical covering map for two-dimensional Lorentzian orbifolds is constructed and applied. The existence of such map shows that any two-dimensional Lorentzian orbifold is very good.
It is proved that there are only two (up to isomorphisms in the category of orbifolds) two-dimensional smooth noncompact orbifolds admitting complete flat Lorentzian ...

Added: April 10, 2019

N. I. Zhukova, E. A. Rogozhina .., Siberian Mathematical Journal 2012 Vol. 53 No. 6 P. 1037-1050

Among closed Lorentzian surfaces, only flat tori admit non-compact full isometry groups. Moreover, for every n > 2 the standard n-dimensional flat torus equipped with canonical metric has a non-compact full isometry Lie group. We show that this fails for n= 2 and classify the flat Lorentzian metrics on the torus with a non-compact full ...

Added: October 19, 2014

N. I. Zhukova, Transformation Groups 2017

We prove an analog of the Lichnerowicz conjecture for compact and noncompact
Riemannian orbifolds. In particular, we prove that any compact Riemannian
orbifold of dimension n >2 with an essential connected Lie group of conformal
transformations is conformally equivalent to the canonical Riemannian orbifold which is the
quotient space of the standard n-dimensional sphere by a finite isometry group ...

Added: April 4, 2017

Vladimir Chigarev, Alexey Kazakov, Arkady Pikovsky, Chaos 2023 Vol. 33 No. 6 Article 063113

We study the heterodimensional dynamics in a simple map on a three-dimensional torus. This map consists of a two-dimensional driving Anosov map and a one-dimensional driven Möbius map, and demonstrates the collision of a chaotic attractor with a chaotic repeller if param- eters are varied. We explore this collision by following tangent bifurcations of the ...

Added: August 30, 2023

Zhukova N., Moscow Mathematical Journal 2018

We introduce a category of rigid geometries on singular spaces which
are leaf spaces of foliations and are considered as leaf manifolds. We
single out a special category F_0 of leaf manifolds containing the orbifold
category as a full subcategory. Objects of F_0 may have non-Hausdorff
topology unlike the orbifolds. The topology of some objects of F_0 does
not satisfy ...

Added: April 2, 2018

Gusein-Zade S., Функциональный анализ и его приложения 2018 Т. 52 № 4 С. 72-85

The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with certain finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. We discuss a universal additive topological invariant of V-manifolds, the universal Euler characteristic. It takes values in the ring ...

Added: October 27, 2020

Zhukova N., Журнал Средневолжского математического общества 2017 Т. 19 № 4 С. 33-44

For any smooth orbifold $\mathcal N$ is constructed a foliated model, which is a foliation
with an Ehresmann, the leaf space of which is the same as $\mathcal N$. We investigate
the relationship relationship between some properties of orbifold and its foliated model.
The article discusses the application to Cartan orbifolds, that is orbifolds endowed with Cartan geometry. ...

Added: February 20, 2018

N. I. Zhukova, Journal of Geometry and Physics 2018 Vol. 132 P. 146-154

We present a new method of investigation of G-structures on orbifolds.
This method is founded on the consideration of a G-structure on an
n-dimensional orbifold as the corresponding transversal
structure of an associated foliation. Using this method we prove the
existence and the uniqueness of a finite dimensional Lie group structures
on the full automorphism group of an elliptic G-structure ...

Added: April 4, 2017

Omelchenko A., Краско Е. С., Discrete Mathematics 2019 Vol. 342 No. 2 P. 584-599

The work that consists of two parts is devoted to the problem of enumerating unrooted r-regular maps on the torus up to all its symmetries. We begin with enumerating near-r- regular rooted maps on the torus, the projective plane and the Klein bottle, as well as some special kinds of maps on the sphere: near-r-regular ...

Added: September 21, 2018

Bonatti C., Minkov S., Alexey Okunev et al., Discrete and Continuous Dynamical Systems 2020 Vol. 40 No. 1 P. 441-465

We present an example of a C1 Anosov diffeomorphism of a two-torus with a physical measure such that its basin has full Lebesgue measure and its support is a horseshoe of zero measure. ...

Added: October 21, 2019

Gusein-Zade S., Manuscripta Mathematica 2018 Vol. 155 No. 3-4 P. 335-353

For a germ of a quasihomogeneous function with an isolated critical point at the origin invariant with respect to an appropriate action of a finite abelian group, H. Fan, T. Jarvis, and Y. Ruan defined the so-called quantum cohomology group. It is considered as the main object of the quantum singularity theory (FJRW-theory). We define ...

Added: October 27, 2020

Бонатти К., Минков С. С., Okunev A. et al., Функциональный анализ и его приложения 2017 Т. 51 № 2 С. 83-86

Мы приводим пример C1-диффеоморфизма Аносова двумерного тора, у которого есть SRB-мера, носитель которой — подкова нулевой меры, а бассейн притяжения имеет полную меру Лебега. ...

Added: October 14, 2018

Kudryashov Y., Kleptsyn V., Ergodic Theory and Dynamical Systems 2015 Vol. 35 No. 03 P. 935-943

We construct a curve in the unstable foliation of an Anosov diffeomorphism such that the holonomy along this curve is defined on all of the corresponding stable leaves. ...

Added: September 30, 2013

Gusein-Zade S., Алгебра и анализ 2021 Т. 33 № 3 С. 73-84

Indices of singular points of a vector field or of a 1-form on a smooth manifold are closely related with the Euler characteristic through the classical Poincar\'e--Hopf theorem. Generalized Euler characteristics (additive topological invariants of spaces with some additional structures) are sometimes related with corresponding analogues of indices of singular points. Earlier, there was defined ...

Added: May 2, 2021

Bagaev A. V., Zhukova N., Journal of Geometry and Physics 2019 Vol. 142 P. 80-91

S.S. Chern conjectured that the Euler characteristic of every closed affine
manifold has to vanish. We present an analog of this conjecture stating that
the Euler-Satake characteristic of any compact affine orbifold is equal to zero.
We prove that Chern's conjecture is equivalent to its analog for
the Euler-Satake characteristic of compact affine orbifolds, and
orbifolds may be ineffective. This ...

Added: April 26, 2019

Omelchenko A., Краско Е. С., Discrete Mathematics 2019 Vol. 342 No. 2 P. 600-614

The second part of the paper is devoted to enumeration of r-regular maps on the torus up to all its homeomorphisms (unsensed maps). We describe in detail the periodic orientation reversing homeomorphisms of the torus which turn out to be representable as glide reflections. We show that considering quotients of the torus with respect to ...

Added: September 21, 2018

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 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

Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.

We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...

Added: March 9, 2014

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019