Related papers: Zakharov-Shabat system and hyperbolic pseudoanalyt…
In this paper we develop the theory of quantum reverse hypercontractivity inequalities and show how they can be derived from log-Sobolev inequalities. Next we prove a generalization of the Stroock-Varopoulos inequality in the…
An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…
The paper deals with topical issues of modern mathematical theory of dynamical chaos and its applications. At present, it is customary to assume that dynamical chaos in finitedimensional smooth systems can exist in three different forms.…
We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples of simply connected quasi-projective varieties that are pseudo-arithmetically hyperbolic. This generalizes…
In this paper, we give sharp Rusak- and Markov-type inequalities for rational functions on several intervals when the system of intervals is a \textquotedblleft rational function inverse image\textquotedblright\, of an interval and those…
Majorana's arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In particular, the approach of Sachs can serve as a…
The application of functional integral methods and the Hubbard--Stratonovich transformation to the Hubbard model is discussed. For the attractive case, using a simple gauge transformation of the superconducting order parameter field, the…
We address the existence of solutions for the inviscid version of the Hall-Vinen-Bekharevich-Khalatnikov equations in 3D, a macro-scale model of superfluidity. This system couples the incompressible Euler equations for the normal fluid and…
In this paper, we prove the Shafarevich conjecture for proper hyperbolic polycurves, which is a higher dimensional analogue of that for proper hyperbolic curves. First, we study theories of proper hyperbolic polycurves over regular schemes.…
We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space with infinitely many branches and variable recurrence time. We show that the decay of correlations of the SRB…
In Euclidean geometry, it is well-known that the $k$-order Voronoi diagram in $\mathbb{R}^d$ can be computed from the vertical projection of the $k$-level of an arrangement of hyperplanes tangent to a convex potential function in…
There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, "hyperbolic". We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption,…
We work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body $P$ in $({\bf R}^+)^d$. We define the {\it logarithmic indicator function} on ${\bf C}^d$: $$H_P(z):=\sup_{ J\in P} \log |z^{…
In this work, we explore the global existence of strong solutions for a class of partially diffusive hyperbolic systems within the framework of critical homogeneous Besov spaces. Our objective is twofold: first, to extend our recent…
We study different notions of quasiconvexity for a subgroup $H$ of a relatively hyperbolic group $G.$ The first result establishes equivalent conditions for $H$ to be relatively quasiconvex. As a corollary we obtain that the relative…
The complete lists of vector hyperbolic equations on the sphere that have integrable third order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability we…
The inverse scattering theory is a basic tool to solve linear differential equations and some Partial Differential Equations (PDEs). Using this theory the Korteweg-de Vries (KdV), the family of evolutionary Non Linear Schrodinger (NLS)…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
We prove that finitely generated relatively hyperbolic groups are bi-exact if and only if all peripheral subgroups are bi-exact. This is a generalization of Ozawa's result which claims that finitely generated relatively hyperbolic groups…
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions…