A 3D Strange Attractor with a Distinctive Silhouette. The Butterfly Effect Revisited

We propose firstly an autonomous system of three first order differential equations which has two nonlinear terms and generating a new and distinctive strange attractor. Furthermore, this new 3D chaotic system performs a new feature of the Sensitive Dependency on Initial Conditions (SDIC) popularized as the Butterfly Effect discovered by Lorenz (1963). We noticed that the variation of the Initial Conditions for our system leads not only to different attractors but also to a singular phenomenon of overlapped attractors.Comment: The paper contains 10 pages, 7 figures (phase portraits and Lyapunov spectrum). Submitted to CHAOS. More materials focusing chaotic attractors at http://chaos-3d.e-monsite.co

A New Hyperchaotic Attractor with Complex Patterns

The paper introduces a new 4d dynamical system leading to a typical 4d strange attractor. Its focal statement appears in its total disconnection from previous 3D nonlinear systems.Comment: 8 pages, 4 Phase portrait projections and 3 Poincare Maps. More materials focusing chaotic attractors at http://chaos-3d.e-monsite.co

The Hunt Hypothesis and the Dividend Policy of the Firm. The Chaotic Motion of the Profits

We have carried out simulations of a financial model of the firm to analyse the validity of the concept of Trade on Equity in dynamics. The results exhibit the ability of the borrowing policy connected to a cautious dividend distribution to inject chaos into the profit motion. The 3D system built with the van der Pol's oscillator produces a new class of strange attractors.Comment: 12 pages, 9 figures (stranges attractors, Poincar=E9 maps, bifurcation diagrams,...). Submitted to the 8th Int. Conf. of the Soc. for Computational Economics, Aix-en-Provence, France, June 27-29, 200

When Aut(A\cal A) and Homeo(Prim(A\cal A)) are homeomorphics

In this paper, we discuss when Aut($\cal A$) and Homeo(Prim($\cal A$)) are homeomorphic, where $\cal A$ is a $C^*$-algebra

Generalized β\beta-Gaussian Ensemble Equilibrium measure method

We investigate $\beta$-Generalized random Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We investigate general method names as equilibrium measure method. When taking $n$ large limit we will see that the asymptotic density of eigenvalues generalize the Wigner semi-circle law

A noncommutative version of the Banach-Stone theorem (II)

In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we give a partial answere to the question 2.1 of [13], and we prove that the structure of the postliminal C*-algebras A determines the topology of its primitive ideals space.Comment: 5 page

Short note on an open problem

In this work, we investigate a problem posed by Feng Qi and Bai-Ni Guo in their paper Complete monotonicities of functions involving the gamma and digamma functions.Comment: 9 pages, 2 figure

Generalized Gaussian Random Unitary Matrices Ensemble

We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite $n$, which will be expressed through an hypergeometric function. When the dimensional of the hermitian matrix begin large enough, we will prove that the statistical density of eigenvalues converge in the tight topology to some probability measure, which generalize the Wigner semi-circle law.Comment: JP Journal of Geometry and Topology 201

Sobolev Freud polynomials

We investigate the uniform asymptotic of some Sobolev orthogonal polynomials. Three term recurrence relation is given, moreover we give a recurrence relation between the so-called Sobolev orthogonal polynomials and Freud orthogonal polynomials

Motives of quadric bundles

This article is about motives of quadric bundles. In the case of odd dimensional fibers and where the basis is of dimension two we give an explicit relative and absolute Chow-K\"unneth decomposition. This shows that the motive of the quadric bundle is isomorphic to the direct sum of the motive of the base and the Prym motive of a double cover of the discriminant. In particular this is a refinement with $\mathbb Q$ coefficients of a result of Beauville concerning the cohomology and the Chow groups of an odd dimensional quadric bundle over $\mathbb P^2$. This Chow-K\"unneth decomposition satisfies Murre's conjectures II and III. This article is a generalization of an article of Nagel and Saito on conic bundles \cite{NS}