Related papers: Generalized Collatz Maps with Almost Bounded Orbit…

The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…

We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…

This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…

Let $A$ be a complex unital Banach algebra. Using a connection between the spectral distance and the growth characteristics of a certain entire map into $A$, we derive a generalization of Gelfand's famous Power Boundedness Theorem.…

In 1994, M. M. Popov [On integrability in F-spaces, Studia Math. no 3, 205-220] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the lp-spaces for 0<p<1,…

In this article, we study bounded-below locally finite $\mathbb{Z}$-graded algebras, which are referred to as commonly graded algebras in literature. Commonly graded algebras have almost similar theory as that of connected graded algebras,…

Let F : V --> V be a self-morphism of a quasiprojective variety defined over a number field K and let P be a point in V(K) with infinite orbit under iteration of F. For each prime ideal p of good reduction, let m_p(F,P) be the size of the…

We study the ``approximate squaring'' map f(x) := x ceiling(x) and its behavior when iterated. We conjecture that if f is repeatedly applied to a rational number r = l/d > 1 then eventually an integer will be reached. We prove this when…

This article is a survey on recent contributions to an effective version of Bautin's theory about the bifurcation of periodic orbits (limit cycles). The analysis of Hopf bifurcations of higher order is possible by use of the return mapping.…

Let $f:(\mathbb{C}^n,0)\mapsto(\mathbb{C}^n,0)$ be a germ of an $n$-dimensional holomorphic map. Assume that the origin is an isolated fixed point of each iterate of $f$. Then $\{\mathcal{N}_q(f)\}_{q=1}^{\infty}$, the sequence of the…

The matrix $p \rightarrow q$ norm is a fundamental quantity appearing in a variety of areas of mathematics. This quantity is known to be efficiently computable in only a few special cases. The best known algorithms for approximately…

We extend Elitzur's theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of {\it dimensional reduction}. We apply the results of this generalization to many systems that are…

Koksma's equidistribution theorem from 1935 states that for Lebesgue almost every $\alpha>1$, the fractional parts of the geometric progression $(\alpha^{n})_{n\geq1}$ are equidistributed modulo one. In the present paper we sharpen this…

In his recent research M. K. Tam (2018) considered a framework for the analysis of iterative algorithms which can be described in terms of a structured set-valued operator. At each point in the ambient space, the value of the operator can…

Using infinite compositions, we solve the general equations $P(\lambda w) = p(w)f(P(w))$ for holomorphic functions $p$ and $f$. We describe the situations in which this equation is palpable; and their effectiveness at describing dynamical…

We characterise absolutely dilatable completely positive maps on the space of all bounded operators on a Hilbert space that are also bimodular over a given von Neumann algebra as rotations by a suitable unitary on a larger Hilbert space…

An error analysis for some Newton-Cotes quadrature formulae is presented. Peano-like error bounds are obtained. They are generally, but not always, better than the usual Peano bounds.

Let $f$ and $g$ be two quasiregular maps in $\mathbb{R}^d$ that are of transcendental type and also satisfy $f\circ g =g \circ f$. We show that if the fast escaping sets of those functions are contained in their respective Julia sets then…

We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…

The Bopp's shifts will be generalized through symplectic formalism. A special procedure, like a "diagonalization", which drives the completely deformed symplectic matrix to the standard symplectic form was found as suggested by…