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Upper bounds for the moduli of polynomial-like maps
Nonlinearity. 2024. Vol. 37. No. 3. Article 035003.
We establish a version of the Pommerenke–Levin–Yoccoz inequality for the modulus of a polynomial-like (PL) restriction of a polynomial and give two applications. First we show that if the modulus of a PL restriction of a polynomial is bounded from below then this restricts the combinatorics of the polynomial. The second application concerns parameter slices of cubic polynomials given by the non-repelling multiplier of a fixed point. Namely, the intersection of the so-called Main Cubioid and the multiplier slice lies in the closure of the principal hyperbolic domain, with possible exception of queer components.
Domrin V. I., Malova H. V., V. Yu. Popov et al., Cosmic Research 2026 Vol. 64 No. 2 P. 238–252
During magnetospheric perturbations a relatively thin current sheet with thickness about several
proton gyroradii forms in the Earth’s magnetotail. In a framework of the kinetic model describing current
sheet thinning in the magnetotail, the processes of its formation are investigated depending on the normal
magnetic field magnitude which affects both the current sheet structure and particle dynamics within ...
Added: April 27, 2026
Tsareva O. O., Malova H. V., V. Yu. Popov et al., Plasma Physics Reports 2026 Vol. 52 No. 2 P. 179–185
The influence of asymmetry of plasma sources on the structure and spatial localization of a superthin
current sheet (STCS) supported by demagnetized electrons is studied using a self-consistent model. The
simulation takes into account the presence of a single plasma source in the northern hemisphere, which
makes the plasma flow asymmetric. It is demonstrated that the asymmetry of ...
Added: April 27, 2026
Pochinka O., Yakovlev E., Shmukler V., Russian Journal of Nonlinear Dynamics 2026
Every discrete dynamical system (cascade) generated by a homeomorphism induces a continuous
dynamic system (flow) — a suspension. However, not every flow is equivalent to a suspension
over a cascade, a necessary and sufficient condition for this is the existence of a global
section for the flow. In the case of the existence, the flow is equivalent to ...
Added: April 24, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 25
We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP ...
Added: April 23, 2026
Kazaryan M., Lando S., Kodaneva N., Journal of Geometry and Physics 2026 No. 225 Article 105841
Weight systems associated to the Lie algebras 𝔤𝔩(N) for N = 1,2,... can be unified into auniversal one. The construction is based on an extension of the 𝔤𝔩(N) weight systems to permutations. This universal weight system takes values in the algebra of polynomials C[N;C1,C2,...] in infinitely many variables. We show that under the substitution Cm ...
Added: April 23, 2026
Kychkin A., Chernitsin I., Прикладная информатика 2026 Т. 21 № 1 С. 40–58
The results of the development of a software microservice embedded in atmospheric air quality monitoring systems to support the identification of industrial pollution sources are presented. The emission and subsequent spread of harmful substances in the lower layers of the atmosphere is dynamic and characterized by high uncertainty due to the specific features of technological ...
Added: April 23, 2026
IEEE, 2026.
Added: April 21, 2026
Galkin O., Galkina S., Ястребова И. Ю., Журнал Средневолжского математического общества 2026 Т. 28 № №1 С. 11–30
Polynomials of least deviation from zero play an important role in the theory and practice of numerical methods. They can be used to solve problems of optimizing the properties of various computational algorithms. Our work is devoted to the study of polynomials of least deviation from zero on a ray in the exponential norm. In ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Petrov I., Doklady Mathematics 2026 Vol. Volume 112 P. S103–S110
This paper examines games on networks with linear best responses, which allow for the analysis of how interaction structures influence agents’ strategic behavior. Special attention is given to intervention issues in such models, particularly in selecting optimal intervention strategies aimed at maximizing the central planner’s objective function. Two main control policies are analyzed: individual agent ...
Added: April 17, 2026
A. V. Pereskokov, Theoretical and Mathematical Physics 2026 Vol. 226 No. 3 P. 470–484
We consider the spectral problem for a hydrogen atom in orthogonal electric and magnetic fields with
an additional self-consistent field. We obtain an asymptotic expansion of self-consistent energy levels.
We find an asymptotic expansion of asymptotic eigenfunctions near the sphere |q| = 2. We calculate the
asymptotics of their norm in the space L2(R3). ...
Added: April 12, 2026
Kolachev N., Адамский А. И., Drozdov D. et al., Моделирование и анализ данных 2026 Т. 16 № 1 С. 157–176
Context and relevance. Despite the widespread adoption of the competency-based approach in higher education, a gap remains between the understanding of competence as a dynamic process and the tools available for its design and management. Dominant practices of learning outcomes assessment rely on static “snapshots,” which limits the possibilities for forecasting and purposeful development of competence. ...
Added: April 10, 2026
Zvereva V., Вопросы экономики 2026 № 4 С. 100–129
This paper examines the hypothesis of asymmetric responses of bank interest rates to restrictive and accommodative monetary policy conducted by the Bank of Russia across different market segments, industries, and macroregions over the period 2017—2025. Using a Markov-switching error-correction model, the paper estimates the effects of monetary policy shocks, households’ inflation expectations, firms’ price expectations, ...
Added: April 8, 2026
Petropavlovsky S., Turkel E., Journal of Computational Physics 2026 Vol. 558 Article 114880
We propose a method for the numerical computation of the 3D time-harmonic scattering about objects of complex shape. Our approach relies on the method of difference potentials combined with the lacunae-based integration of the Helmholtz equation. The former allows to handle curvilinear boundaries of scattering shapes on regular Cartesian grids with no loss of accuracy. ...
Added: April 6, 2026
Romanov I., Шамаев А. С., Математические заметки 2026 Т. 119 № 3 С. 426–432
The existence of a propagation front is proved in the Cauchy problem for a multidimensional wave equation with integral memory and a Rabotnov kernel, which is considered in a certain special case. ...
Added: April 6, 2026
Anna S. Bodrova, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 113 No. 4 Article 045403
We investigate the diffusion coefficients and mean-squared displacements in a polydisperse granular gas in
a homogeneous cooling state by considering the roughness of the particles. We study their dependence on the
normal and tangential restitution coefficients. We show that the motility of particles is strongly affected by their
mechanical properties and surface characteristics. ...
Added: April 5, 2026
Shvedov A. S., Математические заметки 2026 Т. 119 № 4 С. 616–623
В настоящей работе изучается некооперативная игра, в которой фирмы-лидеры конкурируют между собой, выбирая объемы выпуска, и фирмы-последователи конкурируют между собой, также выбирая объемы выпуска. Информация о средних предельных затратах является общедоступной, но текущие предельные затраты фирмы известны только самой фирме. Для этой игры найдены равновесные объемы выпуска. ...
Added: April 3, 2026
- Р. М., Sergei Koltcov, Surkov A. et al., Computers, Materials and Continua 2026 Vol. 86 No. 3 Article 99
Activation pruning reduces neural network complexity by eliminating low-importance neuron activations, yet identifying the critical pruning threshold—beyond which accuracy rapidly deteriorates—remains computationally expensive and typically requires exhaustive search. We introduce a thermodynamics-inspired framework that treats activation distributions as energy-filtered physical systems and employs the free energy of activations as a principled evaluation metric. Phase-transition–like phenomena ...
Added: December 19, 2025
Blokh A., Oversteegen L., Timorin V. et al., Nonlinearity 2025 Vol. 38 No. 7 Article 075014
We describe a locally connected model of the cubic connectedness locus. The model is obtained by constructing a decomposition of the space of critical portraits and collapsing elements of the decomposition into points. This model is similar to a quotient of the combinatorial quadratic Mandelbrot set in which all baby Mandelbrot sets, as well as ...
Added: June 12, 2025
Blokh A., Levin G., Oversteegen L. et al., Communications in Mathematical Physics 2025 Vol. 406 Article 141
The modulus of a polynomial-like (PL) map is an important invariant that controls distortion of the straightening map and, hence, geometry of the corresponding PL Julia set. Lower bounds on the modulus, called complex a priori bounds, are known in a great variety of contexts. For any rational function we complement this by an upper bound ...
Added: May 31, 2025
Blokh A., Oversteegen L., Selinger N. et al., Ergodic Theory and Dynamical Systems 2025 Vol. 45 No. 8 P. 2314–2340
As discovered by W. Thurston, the action of a complex one-variable polynomial on its Julia set can be modeled by a geodesic lamination in the disk, provided that the Julia set is connected. It also turned out that the parameter space of such dynamical laminations of degree two gives a model for the bifurcation locus in the space ...
Added: January 7, 2025
Bizyaev I., Physical Review D - Particles, Fields, Gravitation and Cosmology 2024 Vol. 110 No. 10 P. 104031
This paper investigates the trajectories of neutral particles in the Schwarzschild-Melvin spacetime. After reduction by cyclic coordinates this problem reduces to investigating a two-degree-of-freedom Hamiltonian system that has no additional integral. A classification of regions of possible motion of a particle is performed according to the values of the momentum and energy integrals. Bifurcations of periodic ...
Added: December 10, 2024
Fedor Ozhegov, Reviews in Mathematical Physics 2024 Vol. 36 No. 7 Article 2450017
In this paper, we study Feynman checkers, one of the most elementary models of electron motion. It is also known as a one-dimensional quantum walk or an Ising model at an imaginary temperature. We add the simplest non-trivial electromagnetic field and find the limits of the resulting model for small lattice step and large time, ...
Added: May 17, 2024
Skripchenko A., Успехи математических наук 2023 Т. 78 № 6(474) С. 3–46
Research on dynamical and topological properties of interval exchange transformations and their natural generalizations is an important problem that belongs to the intersection of the several branches of mathematics: dynamical systems, low-dimensional topology, algebraic geometry, number theory and geometric group theory. The goal of the current survey is to make a systematic presentation of the ...
Added: December 28, 2023