Related papers: "Simple Dynamics" conjectures for some real Newton…

Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is…

A general class of Newton algorithms on Gra{\ss}mann and Lagrange-Gra{\ss}mann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local quadratic convergence of the algorithm is shown under a suitable condition…

We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…

Generalized (rational) graph contractions in the framework of a dislocated metric space endowed with a directed graph are investigated. Fixed point results for set-contractions are obtained. We also provide some examples to illustrate our…

A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…

Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…

We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.

While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines the solution of Newton's…

The symmetry properties of the dynamical matrix are well described in multiple classic textbooks. This short paper revisits the issue to demonstrate alternative form of dynamical matrix which explicitly shows its symmetry and reality in…

We propose an approximation to general relativity that captures the main gravitational effects of dynamical importance in supernovae. The conceptual link between this formalism and the Newtonian limit is such that it could likely be…

Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…

The classical gravitational two-body problem is generalized in order to be applicable also to weak gravitational fields. The equation of motion holds both for terrestrial and large cosmic scales, the Newtonian gravitational law represents a…

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…

This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only…

The purpose of this article is to construct a toolbox, in Dynamical Systems, to support the idea that ``whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based…

In this paper, we develop a direct method of moving planes for the fractional Laplacian. Instead of conventional extension method introduced by Caffarelli and Silvestre, we work directly on the non-local operator. Using the integral…

We construct a piecewise onto 3-to-1 dynamical system on the positive quadrant of the unit circle, such that for rational points (which correspond to normalized Primitive Pythagorean Triples), the associated ternary expansion is finite, and…

We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We obtain basic results, both probabilistic and deterministic, draw connections to…