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On the center conditions for analytic monodromic degenerate singularities
https://ddd.uab.cat/record/150541
In this paper we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields can be applied independently that the singularity is algebraic solvable or not, or has characteristic directions or not. We remark that these are the first methods which allows to study monodromic degenerate singularities with characteristic directions. Giné, JaumeFri, 06 May 2016 08:49:23 GMThttps://ddd.uab.cat/record/1505412012Non-autonomous 2-periodic Gumovski-Mira difference equations
https://ddd.uab.cat/record/150532
We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ones differ dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence. Cimà, AnnaFri, 06 May 2016 08:49:22 GMThttps://ddd.uab.cat/record/1505322012Global phase portraits of some reversible cubic centers with collinear or infinitely many singularities
https://ddd.uab.cat/record/150524
We study the reversible cubic vector fields of the form ˙x = −y + ax2 + bxy + cy2 − y(x2 + y2), y˙ = x + dx2 + exy + fy2 + x(x2 + y2), having simultaneously a center at infinity and at the origin. In this paper the subclass of these reversible systems having collinear or infinitely many singularities are classified with respect to topological and diffeomorphic equivalence. Caubergh, MagdalenaFri, 06 May 2016 08:49:22 GMThttps://ddd.uab.cat/record/1505242012Rational first integrals for polynomial vector fields on algebraic hypersurfaces of R^N 1
https://ddd.uab.cat/record/150515
Using sophisticated techniques of Algebraic Geometry Jouanolou in 1979 showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in Rn of degree m is at least n+m−1 n+ n, then the vector field has a rational first integral. Llibre and Zhang used only Linear Algebra provided a shorter and easier proof of the result given by Jouanolou. We use ideas of Llibre and Zhang to extend the Jouanolou result to polynomial vector fields defined on algebraic regular hypersurfaces of Rn+1, this extended result completes the standard results of the Darboux theory of integrability for polynomial vector fields on regular algebraic hypersurfaces of Rn+1. Llibre, JaumeFri, 06 May 2016 08:49:22 GMThttps://ddd.uab.cat/record/1505152012Polynomial first integrals for the Chen and Lu systems
https://ddd.uab.cat/record/150500
Llibre, JaumeFri, 06 May 2016 08:49:21 GMThttps://ddd.uab.cat/record/1505002012Global dynamics in the Poincare ball of the Chen system having invariant algebraic surfaces
https://ddd.uab.cat/record/150498
Llibre, JaumeFri, 06 May 2016 08:49:21 GMThttps://ddd.uab.cat/record/1504982012Global Classification of a class of Cubic Vector Fields whose canonical regions are period annuli
https://ddd.uab.cat/record/150445
Caubergh, MagdalenaFri, 06 May 2016 08:30:49 GMThttps://ddd.uab.cat/record/1504452011Limit cycles of discontinuous piecewise linear differential systems
https://ddd.uab.cat/record/150439
We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in Rn perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed. Cardin, Pedro ToniolFri, 06 May 2016 08:30:49 GMThttps://ddd.uab.cat/record/1504392011A survey on the blow up technique
https://ddd.uab.cat/record/150433
The blow up technique is widely used in desingularization of degenerate singular points of planar vector fields. In this survey we give an overview of the different types of blow up and we illustrate them with many examples for better understanding. Moreover, we introduce a new generalization of the classical blow up. Álvarez Torres, María JesúsFri, 06 May 2016 08:30:49 GMThttps://ddd.uab.cat/record/1504332011Electrically small resonators for planar metamaterial, microwave circuit and antenna design :: a comparative analysis
https://ddd.uab.cat/record/147285
Planar metamaterials and many microwave circuits and antennas are designed by means of resonators with dimensions much smaller than the wavelength at their resonance frequency. There are many types of such electrically small resonators, and the main purpose of this paper is to compare them as building blocks for the implementation of microwave components. Aspects such as resonator size, bandwidth, their circuit models when they are coupled to transmission lines (as is usually required), as well as key applications, will be considered. Durán-Sindreu Viader, MiguelWed, 02 Mar 2016 12:22:47 GMThttps://ddd.uab.cat/record/1472852012Symmetry-Related Electromagnetic Properties of Resonator-Loaded Transmission Lines and Applications
https://ddd.uab.cat/record/146255
This paper reviews the recent progress in the analysis and applications of the symmetry-related electromagnetic properties of transmission lines loaded with symmetric configurations of resonant elements. It will be shown that the transmission characteristics of these reactively loaded lines can be controlled by the relative orientation between the line and the resonant elements. Two main types of loaded lines are considered: (i) resonance-based structures; and (ii) frequency-splitting structures. In resonance-based transmission lines, a line is loaded with a single resonant (and symmetric) element. For a perfectly symmetric structure, the line is transparent if the line and resonator exhibit symmetry planes of different electromagnetic nature (electric or magnetic wall), whereas the line exhibits a notch (resonance) in the transmission coefficient if the symmetry planes behave as either electric or magnetic walls (symmetric configuration), or if symmetry is broken. In frequency-splitting lines, paired resonators are typically loaded to the transmission line; the structure exhibits a single notch for the symmetric configuration, whereas generally two split notches appear when symmetry is disrupted. Applications of these structures include microwave sensors (e. g. , contactless sensors of spatial variables), selective mode suppressors (of application in common-mode suppressed differential lines, for instance) and spectral signature barcodes, among others. Naqui Garolera, JordiThu, 11 Feb 2016 15:17:54 GMThttps://ddd.uab.cat/record/1462552015Hopf bifurcation in the full repressilator equations
https://ddd.uab.cat/record/145362
In this paper we prove that the full repressilator equations, in dimension six undergo a supercritical Hopf bifurcation. Buzzi, Claudio AguinaldoTue, 12 Jan 2016 16:38:11 GMThttps://ddd.uab.cat/record/1453622015Limit cycles bifurcating from the periodic orbits of a discontinuous piecewise linear differential center with two zones
https://ddd.uab.cat/record/145336
We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0 we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that its is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential systems formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N ≥ 2 when p is a real or virtual center. Llibre, JaumeTue, 12 Jan 2016 16:38:10 GMThttps://ddd.uab.cat/record/1453362015Normal Forms for Polynomial Differential Systems in R^3 Having an Invariant Quadric and a Darboux Invariant
https://ddd.uab.cat/record/145333
We give the normal forms of all polynomial differential systems in R^3 which have a nondegenerate or degenerate quadric as an invariant algebraic surface. We also characterize among these systems those which have a Darboux invariant constructed uniquely using the invariant quadric, giving explicitly their expressions. As an example, we apply the obtained results in the determination of the Darboux invariants for the Chen system with an invariant quadric. Llibre, JaumeTue, 12 Jan 2016 16:38:10 GMThttps://ddd.uab.cat/record/1453332015A simple solution to the Braga-Mello conjecture
https://ddd.uab.cat/record/145328
Recently Braga and Mello conjectured that for a given n N there is a piecewise linear system with two zones in the plane with exactly n limit cycles. In this paper, we prove a result from which the conjecture is an immediate consequence. Several explicit examples are given where location and stability of limit cycles are provided. Novaes, Douglas D.Tue, 12 Jan 2016 16:38:09 GMThttps://ddd.uab.cat/record/1453282015Medium amplitude limit cycles of some classes of generalized Liénard systems
https://ddd.uab.cat/record/145317
Rebollo-Perdomo, SalomónTue, 12 Jan 2016 16:38:08 GMThttps://ddd.uab.cat/record/1453172015On the dynamics of a system that bridges the gap between Lorenz and Chen systems
https://ddd.uab.cat/record/145306
A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we also can describe the global dynamics in the whole R 3 using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family. Llibre, JaumeTue, 12 Jan 2016 16:38:08 GMThttps://ddd.uab.cat/record/1453062015Less is more :: effects of the amount of information and its presentation in the recall and reception of audio described characters
https://ddd.uab.cat/record/129665
Audio description is a discipline within Translation Studies aimed at making audio visual products and events accessible to blind and visually impaired audiences. Works of art, TV programs, films and stage arts are audio described in order to guarantee that anyone, regardless of his/her visual capacity, can enjoy them. In the case of films, it consists of a verbal description of visual details such as settings and characters (what they look like, what they do and how they do it) provided to the audience in those parts of the movie where no relevant sounds or dialogues are heard. The nature of audio description, in which all the information is presented auditorily and at the fast pace usually imposed by films, might pose some challenges on users' memory. This paper is an attempt to explore this issue empirically by focusing on audio described characters. It presents a reception study designed to explore how the amount of information included in the audio description of characters and its presentation have an effect on users' recall. Results showed that limiting the information in the descriptions and dividing it into short units delivered at different stages of the AD favored users' memory. Fresno Cañada, NazaretWed, 25 Feb 2015 21:38:26 GMThttps://ddd.uab.cat/record/1296652014