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Distribuyendo oportunidades :: El impacto de los agrupamientos escolares en la experiencia de los estudiantes
http://ddd.uab.cat/record/169501
El presente artículo realiza una revisión de la literatura de investigación centrada en la estratificación escolar interna y los procesos de selección del alumnado, con el fin de discernir los espacios de aprendizaje y de socialización diferenciados que existen dentro de las propias escuelas. Considera los datos empíricos que las investigaciones aportan acerca de las diversas formas de agrupamiento de los estudiantes, los argumentos y criterios sobre los que se sustentan y el impacto que estos tienen sobre los resultados académicos y la experiencia escolar. Presenta también las investigaciones que en España han abordado esta estratificación y señala el impacto sobre los estudiantes de esta estrategia organizativa escolar. ; This article proposed carries out a revision of the literature of research on school internal stratification and the selection processes of students, with the purpose of discerning the different spaces of learning and socialization that exist inside the school itself. It considers the empirical data that researches provide about the different forms of students grouping, the arguments and criteria on which they hold and the impact that these forms of students grouping have on the academic results and school experience. It also shows the researches that in Spain have dealt this stratification and points the impact on the students of this school organization strategy. Pàmies Rovira, JordiMon, 23 Jan 2017 15:57:31 GMThttp://ddd.uab.cat/record/169501Uniform isochronous cubic and quartic centers: Revisited
http://ddd.uab.cat/record/169500
In this paper we completed the classification of the phase portraits in the Poincaré disc of uniform isochronous cubic and quartic centers previously studied by several authors. There are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively. Artés, Joan CarlesMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169500Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
http://ddd.uab.cat/record/169499
In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4. Benterki, RebihaMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169499On the minimum positive entropy for cycles on trees
http://ddd.uab.cat/record/169498
Alsedà, LluísMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169498Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle
http://ddd.uab.cat/record/169497
The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. Even though many papers have been written on this class of systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilbert’s 16th problem [Hilbert, 1900, 1902], are still open for this family. In this article, we make a global study of the family QTS of all real quadratic polynomial differential systems which have a finite semi-elemental triple saddle (triple saddle with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this normal form. This bifur- cation diagram yields 27 phase portraits for systems in QTS counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set and we present the phase portraits on the Poincar ́e disk. The bifurcation set is not just algebraic due to the presence of a surface found numerically, whose points correspond to connections of separatrices. Artés, Joan CarlesMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169497On a Class of Invariant Algebraic Curves for Kukles Systems
http://ddd.uab.cat/record/169496
Osuna, OsvaldoMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169496Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory
http://ddd.uab.cat/record/169495
We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. The Hamiltonian system here studied comes either from the analyze of the galactic dynamics, or from the motion of the atomic particles in physics. Lembarki, Fatima E.Mon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169495Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure
http://ddd.uab.cat/record/169494
A ratio–dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E ∗ at the positive octant is unstable. Here we characterize the existence of Hopf bifurcations for the systems. In particular we provide a positive answer to the above question showing for such models the existence of small–amplitude Hopf limit cycles being the equilibrium point E ∗ unstable. Llibre, JaumeMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169494Analytic reducibility of nondegenerate centers: Cherkas systems
http://ddd.uab.cat/record/169493
Giné, JaumeMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169493First integrals and phase portraits of planar polynomial differential cubic systems with the maximum number of invariant straight lines
http://ddd.uab.cat/record/169492
In the article LliVul2006 the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial differential systems can have if this number is finite. Here we complete the classification given in LliVul2006 by adding a new class of such cubic systems and for each one of these 24 such classes we perform the corresponding first integral as well as its phase portrait. Moreover we present necessary and sufficient affine invariant conditions for the realization of each one of the detected classes of cubic systems with maximum number of invariant straight lines when this number is finite. Bujac, CristinaMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169492Periods of continuous maps on some compact spaces
http://ddd.uab.cat/record/169489
The objective of this paper is to provide information on the set of periodic points of a continuous self--map defined in the following compact spaces: S^n (the n--dimensional sphere), S^n S^m (the product space of the n--dimensional with the m--dimensional spheres), CP^n (the n--dimensional complex projective space) and HP^n (the n--dimensional quaternion projective space). We use as main tool the action of the map on the homology groups of these compact spaces. Guirao, Juan Luis GarciaMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169489Newton's method for symmetric quartic polynomials
http://ddd.uab.cat/record/169488
We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials p_a,b(z)=z^4 az^3 bz^2 az 1, where a and b are real parameters. We divide the parameter plane (a,b) R^2 into twelve open and connected regions where p, p' and p'' have simple roots. In each of these regions we focus on the study of the Newton's operator acting on the Riemann sphere. Campos, BeatrizMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169488A quasiperiodically forced skew-product on the cyclinder without fixed-curves
http://ddd.uab.cat/record/169487
In [FJJK] the Sharkovskiı Theorem was extended to periodic orbits of strips of quasiperiodic skew products in the cylinder. In this paper we deal with the following natural question that arises in this setting: Does Sharkovskiı Theorem holds when restricted to curves instead of general strips? We answer this question in the negative by constructing a counterexample: We construct a map having a periodic orbit of period 2 of curves (which is, in fact, the upper and lower circles of the cylinder) and without any invariant curve. In particular this shows that there exist quasiperiodic skew products in the cylinder without invariant curves. [FJJK] Roberta Fabbri, Tobias Jäger, Russell Johnson, and Gerhard Keller. A Sharkovskii-type theorem for minimally forced interval maps. Topol. Methods Nonlinear Anal. , 26(1):163--188, 2005. Alsedà, LluísMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169487Tongues in Degree 4 Blaschke Products
http://ddd.uab.cat/record/169486
The goal of this paper is to investigate the family of Blasche products B_a(z)=z^3-a1- which is a rational family of perturbations of the doubling map. We focus on the tongue-like sets which appear in its parameter plane. We first study their basic topological properties and afterwords we investigate how bifurcations take place in a neighborhood of their tips. Finally we see how the period one tongue extends beyond its natural domain of definition. Canela, JordiMon, 23 Jan 2017 15:21:48 GMThttp://ddd.uab.cat/record/169486Canards Existence in Memristor’s Circuits
http://ddd.uab.cat/record/169485
The aim of this work is to propose an alternative method for determining the condition of existence of “canard solutions” for three and four-dimensional singularly perturbed systems with only one fast variable in the folded saddle case. This method enables to state a unique generic condition for the existence of “canard solutions” for such three and four-dimensional singularly perturbed systems which is based on the stability of folded singularities of the normalized slow dynamics deduced from a well-known property of linear algebra. This unique generic condition is perfectly identical to that provided in previous works. Application of this method to the famous three and four-dimensional memristor canonical Chua’s circuits for which the classical piecewise-linear characteristic curve has been replaced by a smooth cubic nonlinear function according to the least squares method enables to show the existence of “canard solutions” in such Memristor Based Chaotic Circuits. Ginoux, Jean-MarcMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169485The number of polynomial solutions of polynomial Riccati equations
http://ddd.uab.cat/record/169484
Consider real or complex polynomial Riccati differential equations a(x) y=b_0(x) b_1(x)y b_2(x)y^2 with all the involved functions being polynomials of degree at most . We prove that the maximum number of polynomial solutions is 1 (resp. 2) when 1 (resp. =0) and that these bounds are sharp. For real trigonometric polynomial Riccati differential equations with all the functions being trigonometric polynomials of degree at most 1 we prove a similar result. In this case, the maximum number of trigonometric polynomial solutions is 2 (resp. 3) when 2 (resp. =1) and, again, these bounds are sharp. Although the proof of both results has the same starting point, the classical result that asserts that the cross ratio of four different solutions of a Riccati differential equation is constant, the trigonometric case is much more involved. The main reason is that the ring of trigonometric polynomials is not a unique factorization domain. Gasull, ArmengolMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169484When parallels and meridians are limit cycles for polynomial vector fields on quadrics of revolution in the euclidean 3-space
http://ddd.uab.cat/record/169483
We study polynomial vector fields of arbitrary degree in R^3 with an invariant quadric of revolution. We characterize all the possible configurations of invariant meridians and parallels that these vector fields can exhibit. Furthermore we analyze when these invariant meridians and parallels can be limit cycles. Dias, Fabio ScalcoMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169483On the number of limit cycles for perturbed pendulum equations
http://ddd.uab.cat/record/169482
We consider perturbed pendulum-like equations on the cylinder of the form x (x)= _=0^mQ_n, (x) x^ where Q_n, are trigonometric polynomials of degree n, and study the number of limit cycles that bifurcate from the periodic orbits of the unperturbed case =0 in terms of m and n. Our first result gives upper bounds on the number of zeros of its associated first order Melnikov function, in both the oscillatory and the rotary regions. These upper bounds are obtained expressing the corresponding Abelian integrals in terms of polynomials and the complete elliptic functions of first and second kind. Some further results give sharp bounds on the number of zeros of these integrals by identifying subfamilies which are shown to be Chebyshev systems. Gasull, ArmengolMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169482Averaging methods of arbitrary order, periodic solutions and integrability
http://ddd.uab.cat/record/169481
In this paper we provide an arbitrary order averaging theory for higher dimensional periodic analytic differential systems. This result extends and improves results on averaging theory of periodic analytic differential systems, and it unifies many different kinds of averaging methods. Applying our theory to autonomous analytic differential systems, we obtain some conditions on the existence of limit cycles and integrability. For polynomial differential systems with a singularity at the origin having a pair of pure imaginary eigenvalues, we prove that there always exists a positive number N such that if its first N averaging functions vanish, then all averaging functions vanish, and consequently there exists a neighborhood of the origin filled with periodic orbits. Consequently if all averaging functions vanish, the origin is a center for n = 2. Furthermore, in a punctured neighborhood of the origin, the system is C^ completely integrable for n > 2 provided that each periodic orbit has a trivial holonomy. Finally we develop an averaging theory for studying limit cycle bifurcations and the integrability of planar polynomial differential systems near a nilpotent monodromic singularity and some degenerate monodromic singularities. Giné, JaumeMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169481On the analytic integrability of the Liénard analytic differential systems
http://ddd.uab.cat/record/169480
We consider the Li\'enard analytic differential systems x = y, y =-g(x) -f(x)y, where f,g: R R are analytic functions and the origin is an isolated singular point. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the origin and the existence of global analytic first integrals. Llibre, JaumeMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169480Continua of periodic points for planar integrable rational maps
http://ddd.uab.cat/record/169479
We present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used for other authors and apply when the maps are birational and the generic level sets of the corresponding first integrals have either genus 0 or 1. As far as we know, the third one is new and it works for rational maps without imposing topological properties to the invariant level sets. It is based on a computational point of view, and relies on the use of resultants in a suitable setting. We apply them to several examples, including the 2-periodic Lyness composition maps and some of the celebrated McMillan-Gumowski-Mira maps. Gasull, ArmengolMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169479Limit cycles of linear vectors on manifolds
http://ddd.uab.cat/record/169478
It is well known that linear vector fields on the manifold R^n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C^1 connected manifold. Llibre, JaumeMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169478Centers: their integrability and relations with the divergence
http://ddd.uab.cat/record/169477
This is a brief survey on the centers of the analytic differential systems in R^2. First we consider the kind of integrability of the different types of centers, and after we analyze the focus--center problem, i. e. how to distinguish a center from a focus. This is a difficult problem which is not completely solved. We shall present some recent results using the divergence of the differential system. Llibre, JaumeMon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169477Center cyclicity of a family of quartic polynomial differential system
http://ddd.uab.cat/record/169476
In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as \[ = i z z (A z^2 B z C ^2 ),\] where A,B,C C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp. García, Isaac A.Mon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169476New results on averaging theory and applications
http://ddd.uab.cat/record/169475
The usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i. e. the Jacobian of the averaged function in it is zero, the classical averaging theory does not provide information about the periodic solution associated to a non simple zero. Here we provide sufficient conditions in order that the averaging theory can be applied also to non simple zeros for studying their associated periodic solutions. Additionally we do two applications of this new result for studying the zero--Hopf bifurcation in the Lorenz system and in the Fitzhugh--Nagumo system. Cândido, Murilo R.Mon, 23 Jan 2017 15:21:47 GMThttp://ddd.uab.cat/record/169475