Related papers: Herman Rings: Structure, Dynamics, and Open Proble…
The study of homological invariants such as Tor, Ext and local cohomology modules constitutes an important direction in commutative algebra. Explicit descriptions of these invariants are notoriously difficult to find and often involve…
We describe bounded, holomorphic functions on the complex 2-disc, that admit meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski…
Recently, Benini et al. showed that, in simply connected wandering domains of entire functions, all pairs of orbits behave in the same way relative to the hyperbolic metric, thus giving us our first insight into the general internal…
The radial motion of matter in a centrally symmetric gravitational field in a comoving reference frame is investigated for a realistic equation of state of matter. The dynamics of the formation of an event horizon are investigated.
We consider Bergman spaces and variations of them in one or several complex variables. For some domains we show that in these spaces the generic function is totally unbounded and hence non - extendable. We also show that the generic…
In general the endomorphisms of a non-abelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group which are endomorphisms when…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical…
The Humbert-Bessel are multi-index functions with various applications in electromagnetism. New families of functions sharing some similarities with Bessel functions are often introduced in the mathematical literature, but at a closer…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
We report the counter-intuitive instability of charged elastic rings, and the persistence of sinusoidal deformations in the lowest-energy configurations by the combination of high-precision numerical simulations and analytical perturbation…
We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the…
This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlev\'e equations, for which the developments of the last two…
We study the ring of rational functions admitting a continuous extension to the real affine space. We establish several properties of this ring. In particular, we prove a strong Nullstelensatz. We study the scheme theoretic properties and…
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…
We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…
Studies on the dynamical properties of the $\sigma$ meson are reviewed and discussed. The important role of fundamental principles such as analyticity, unitarity and crossing symmetry played in the studies are stressed.
Regluing is a topological operation that helps to construct topological models for rational functions on the boundaries of certain hyperbolic components. It also has a holomorphic interpretation, with the flavor of infinite dimensional…
We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization operator. We give a few illustrations in dynamics in one and…
Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas…