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Monotonicity and non-monotonicity regions of topological entropy for Lorenz-like families with infinite derivatives
Applied Mathematics and Nonlinear Sciences. 2020. Vol. 5. No. 2. P. 293-306.
Malkin M., Safonov K.
We study behavior of the topological entropy as the function of parameters for two-parameter family of symmetric Lorenz maps T_{c,epsilon}(x)=(-1+c|x|^{1-epsilon}) sgn(x). This is the normal form for splitting the homoclinic loop in systems which have a saddle equilibrium with one-dimensional unstable manifold and zero saddle value. Due to L.P. Shilnikov results, such a bifurcation corresponds to the birth of Lorenz attractor (when the saddle value becomes positive). We indicate those regions in the bifurcation plane where the topological entropy depends monotonically on the parameter c, as well as those for which the monotonicity does not take place. Also, we indicate the corresponding bifurcations for the Lorenz attractors.
Publication based on the results of:
Gonchenko S. V., Gonchenko A. S., Kazakov A. et al., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2018 Vol. 28 No. 11 P. 1830036-1-1830036-29
The paper is devoted to topical issues of modern mathematical theory of dynamical chaos and its applications. At present, it is customary to assume that dynamical chaos in finite-dimensional smooth systems can exist in three different forms. This is dissipative chaos, the mathematical image of which is a strange attractor; conservative chaos, for which the ...
Added: October 26, 2018
Blank M., Nonlinearity 2012 Vol. 25 No. 12 P. 3389-3408
We study ergodic properties of a family of traffic maps acting in
the space of bi-infinite sequences of real numbers. The corresponding
dynamics mimics the motion of vehicles in a simple traffic flow, which
explains the name. Using connections to topological Markov chains we obtain
nontrivial invariant measures, prove their stochastic stability, and
calculate the topological entropy. Technically these results ...
Added: November 26, 2014
Е.В. Жужома, Исаенкова Н. В., В.С. Медведев, Журнал Средневолжского математического общества 2018 Т. 20 № 1 С. 23-29
In the paper we construct some example of smooth dieomorphism of closed manifold. This dieomorphism has one-dimensional (in topological sense) basic set with stable invariant manifold of arbitrary nonzero dimension and the unstable invariant manifold of arbitrary dimension not less than two. The basic set has a saddle type, i.e. is neither attractor nor repeller. ...
Added: May 25, 2018
Kazakov A., Козлов А. Д., Журнал Средневолжского математического общества 2018 Т. 20 № 2 С. 187-198
In the paper a new method of constructing of three-dimensional flow systems with different chaotic attractors is presented. Using this method, an example of three-dimensional system possessing an asymmetric Lorenz attractor is obtained. Unlike the classical Lorenz attractor, the observed attractor does not have symmetry. However, the discovered asymmetric attractor, as well as classical one, ...
Added: October 26, 2018
Малкин М. И., Safonov K., Chaos 2021 Vol. 31 Article 043107
This paper deals with one-dimensional factor maps for the geometric model of Lorenz-type attractors in the form of two-parameter family of Lorenz maps on the interval 𝐼=[−1,1]I=[−1,1] given by 𝑇𝑐,𝜈(𝑥)=(−1+𝑐⋅|𝑥|𝜈)⋅𝑠𝑖𝑔𝑛(𝑥)Tc,ν(x)=(−1+c⋅|x|ν)⋅sign(x). This is the normal form for splitting the homoclinic loop with additional degeneracy in flows with symmetry that have a saddle equilibrium with a one-dimensional unstable manifold. Due ...
Added: September 21, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
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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 ...
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Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
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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. ...
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Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
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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
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
Кокоулина М. В., Епифанова А. С., Pelinovsky E. et al., Труды НГТУ им. Р.Е. Алексеева 2020 № 3 С. 28-41
Purpose: to analyze the dynamics of COVID-19 development using a generalized stochastic logistic equation to esti-mate the number of probable peaks in coronavirus incidence and to evaluate the nature of the scatter of the generalized logistic model coefficients.
Design/methodology/approach: we use a logistic model based on a generalized first-order logistic equation. The data on the incidence ...
Added: September 29, 2020
Семин С. В., Kurkina O. E., Kurkin A. A. et al., Труды НГТУ им. Р.Е. Алексеева 2012 № 2(95) С. 48-65
Purpose: Numerical modeling of internal baroclinic disturbances of different shapes in a model lake with variable depth, analysis of velocity field of wave-induced current, especially in the near-bed layer.
Approach: The study is carried out with the use of numerical full nonlinear nonhydrostatic model for stratified fluid.
Findings: The full nonlinear numerical modeling of internal wave dynamics ...
Added: October 6, 2012
49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 2 P. 168-173
The parameters of unstable short-living isotopes are studied from
the mathematical point of view. The values of the chemical potential
and activity parameters that determine the neutron halo arising when
the neutron separates from the nucleus of an unstable isotope are
calculated. The analogy between nuclear physics and economics is
considered from the point of view of such parameters as ...
Added: August 25, 2019
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
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
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 ...
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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
Bershtein M., Feigin B. L., Merzon G., Selecta Mathematica, New Series 2018 Vol. 24 No. 1 P. 21-62
We study plane partitions satisfying condition a_{n+1,m+1}=0 (this condition is called “pit”) and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions. Such plane partitions label the basis vectors in certain representations of quantum toroidal gl1 algebra, therefore our formulas can be interpreted as the characters of ...
Added: October 24, 2018