Related papers: Herman Rings: Structure, Dynamics, and Open Proble…
Following ideas from a preprint of the second author, see [2], we investigate relations of dynamical Teichmuller spaces with dynamical objects. We also establish some connections with the theory of deformations of inverse limits and…
We discuss the problem of the existence of envelopes of holomorphy of the A-crosses, which leads us to the far-reaching generalizations of the famous Hartogs theorem. We also take under consideration the issue of the existence of "nice"…
This article is a contribution to the study of superintegrable Hamiltonian systems with magnetic fields on the three-dimensional Euclidean space $\mathbb{E}_3$ in quantum mechanics. In contrast to the growing interest in complex…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
As a cornerstone of functional analysis, Hahn Banach theorem constitutes an indispensable tool of modern analysis where its impact extends beyond the frontiers of linear functional analysis into several other domains of mathematics,…
Given a commutative ring with identity $R$, many different and interesting operations can be defined over the set $H_R$ of sequences of elements in $R$. These operations can also give $H_R$ the structure of a ring. We study some of these…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
This paper is devoted to establish sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extend some results for entire functions to meromorphic functions. Actually, we shall mainly…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
In his celebrated counterexample to the KAM theorem, Herman introduced a perturbation of an integrable system consisting of two components: a hyperbolic term and a bump function. He also remarked that it was unclear whether the bump…
This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.
Cohomological equations appear frequently in dynamical systems. One of the most classical examples is the Liv\v{s}ic equation $$ v(x) = \alpha \circ F(x) - \alpha(x).$$ The existence and regularity of its solutions $\alpha$ is well…
In calculus, an indefinite integral of a function $f$ is a differentiable function $F$ whose derivative is equal to $f$. In present paper, we generalize this notion of the indefinite integral from the ring of real functions to any ring. The…
In this paper we study homoclinic tangles formed by transversal intersections of the stable and the unstable manifold of a {\it non-resonant, dissipative} homoclinic saddle point in periodically perturbed second order equations. We prove…
In a previous paper we began our analysis on the role of non self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growing interest on this topic and on some recent results on…
We show that any uniformly escaping and wandering dynamics of a holomorphic function on a compact subset of the plane can be realised by a transcendental meromorphic function on $\mathbb{C}$. More precisely, let $\varphi$ be a holomorphic…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…