Related papers: Dynamical generation of parameter laminations
The classical modular polynomial for $j$-invariants describes the relation between two elliptic curves connected by isogenies. This polynomial has been applied to various algorithms in computational number theory, such as point counting on…
Direct look at the celebrated "chaotic" Mandelbrot Set in Fig..\ref{Mand2} immediately reveals that it is a collection of almost ideal circles and cardioids, unified in a specific {\it forest} structure. In /hep-th/9501235 a systematic…
We explore a scenarios where topcolor-like dynamics operates in the presence of fourth generation matter fields. Using the Minimal Walking Technicolor as a concrete basis for model building, we construct explicit models and confront them…
In this note, we intend to produce all latin squares from one of them using suitable move which is defined by small trades and do the similar work on 4-cycle systems. These problems, reformulate as finding basis for the kernel of special…
We argue that discrete dynamics has natural links to the theory of analytic functions. Most important, bifurcations and chaotic dynamical properties are related to intersections of algebraic varieties. This paves the way to identification…
A linear principal minor polynomial or lpm polynomial is a linear combination of principal minors of a symmetric matrix. By restricting to the diagonal, lpm polynomials are in bijection to multiaffine polynomials. We show that this…
We introduce the exciting field of complex dynamics at an undergraduate level while reviewing, reinforcing, and extending the ideas learned in an typical first course on complex analysis. Julia sets and the famous Mandelbrot set will be…
The generation of fractals and study of the dynamics of polynomials is one of the emerging and interesting field of research nowadays. We introduce in this paper the dynamics of polynomials z^ n - z + c = 0 for n>=2 and applied Jungck…
Subalgebras of upper triangular matrix algebras have played a fundamental role in the classification of minimal varieties of polynomial growth. Such classification has become a source of study in recent years since it leads to the more…
In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a flat structure, similar to geodesic laminations on hyperbolic surfaces. Here is a sequel to this article that aims at defining transversal measures on flat…
The Tautological Lamination arises in holomorphic dynamics as a combinatorial model for the geometry of 1-dimensional slices of the Shift Locus. In each degree $q$ the tautological lamination defines an iterated sequence of partitions of…
We describe the "hyperbolic" properties of a riemann surface lamination M canonically associated to every compact three manifolds of curvature less than 1. More precisely, if the geodesic flow is the phase space attached to an ordinary…
We introduce a system of parameters for the Monte Carlo generation of Lorentz invariant phase space that is particularly well-suited to the treatment of the infrared divergences that occur in the most singular, Born-like configurations of…
The famous MLC Conjecture states that the Mandelbrot set is locally connected, and it is considered by many to be the central conjecture in one-dimensional complex dynamics. Among others, it implies density of hyperbolicity in the quadratic…
We consider perturbations of the complex quadratic map $ z \to z^2 +c$ and corresponding changes in their quasi-Mandelbrot sets. Depending on particular perturbation, visual forms of quasi-Mandelbrot set changes either sharply (when the…
Let $f$ be a rational map with degree $d\geq 2$ whose Julia set is connected but not equal to the whole Riemann sphere. It is proved that there exists a rational map $g$ such that $g$ contains a buried Julia component on which the dynamics…
We give examples of infinitely renormalizable quadratic polynomials $F_c: z\maps to z^2+c$ with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrar y close to 1. The combinatorics of the renormalization involved is…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
We describe a primary limb structure in the connectedness locus of complex cubic polynomials, where the limbs are indexed by the periodic points of the doubling map $t \mapsto 2t \ (\operatorname{mod} {\mathbb Z})$. The main renormalization…
We consider the relations of generalized commutativity in the algebra of formal series $ M_q (x^i ) $, which conserve a tensor $ I_q $-grading and depend on parameters $ q(i,k) $ . We choose the $ I_q $-preserving version of differential…