Usos del pretérito perfecto simple y compuesto en la lengua Española. Un análisis comparativo de distintas variedades

Treballs Finals de Grau de Filologia Hispànica. Facultat de Filologia. Universitat de Barcelona, Curs: 2016-2017, Tutora: Mª Rosa Vila PujolA lo largo de la carrera, uno de los ámbitos que me ha interesado más es el de la reflexión lingüística, vinculada a asignaturas como Gramática Descriptiva de la lengua española, Historia de la lengua española o Sintaxis; así como, el tema de la variación dialectal, relacionada con la asignatura de Español de América. En este sentido, el poder constatar la evolución de las lenguas, su vivencia y su carácter cambiante ha sido uno de los temas que más me ha motivado. Desde la perspectiva de mi futuro profesional, es importante contemplar la figura del docente en centros educativos con una diversidad de procedencia cultural y lingüística del alumnado. De este hecho, se desprende el valor enriquecedor que ha supuesto para mí el poder comprender los usos del pretérito perfecto simple y compuesto en distintas zonas hispanohablantes que, a su vez, son tan frecuentes tanto en el registro formal como informal. Es cierto que existen un número muy amplio de estudios relacionados con estos dos tiempos verbales, puesto que es un tema que, pese a que lleva años analizándose, sigue siendo un tema sometido a debate. Así pues, actualmente, hay muchas investigaciones que siguen insistiendo en este aspecto, en el cual se enmarca este trabajo. El proceso de trabajo seguido ha partido de una primera fase de búsqueda documental y análisis de la información existente. La síntesis de las ideas fundamentales se ha plasmado en la primera parte del trabajo y las diversas lecturas realizadas orientaron la elaboración de un estudio de campo que, sin pretender ser representativo, nos permitiera analizar la realidad lingüística de estos dos tiempos verbales..

On the Darboux integrability of a cubic CRNT model in R^5

Agraïments: Portuguese National Funds through FCT - Fundacâo para a Ciência e a Tecnologia within projects PTDC/MAT/117106/2010 and PEst-OE/EEI/LA0009/2013 (CAMGSD).We study the Darboux integrability of a differential system with parameters coming from a chemical reaction model in R5. We find all its Darboux polynomials and exponential factors and we prove that it is not Darboux integrable

Analytic integrability of a class of planar polynomial differential systems

Agraïments: The second author was supported by Portuguese National Funds through FCT - Fundacâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD.In this paper we find necessary and sufficient conditions in order that the differential systems of the form ˙x = xf(y), ˙y = g(y), with f and g polynomials, have a first integral which is analytic in the variable x and meromorphic in the variable y. We also characterize their analytic first integrals in both variables x and y. These polynomial differential systems are important because after a convenient change of variables they contain all quasi-homogeneous polynomial differential systems in R2

On the global dynamics of a finance model

Agraïments: The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.Recently several works have studied the following model of finance $$x= z (y-a) x, y= 1-b y -x^2, z= -x -c z,$$ where a, b and c are positive real parameters. We study the global dynamics of this polynomial differential system, and in particular for a one--dimensional parametric subfamily we show that there is an equilibrium point which is a global attractor

On the analytic integrability of the Liénard analytic differential systems

Agraïments: The second author is supported by Portuguese National Funds through FCT - Fundaçâo para a Ciência e a Tecnologia trough UID/MAT/04459/20We consider the Liénard 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

On the dynamics of a model with coexistence of three attractors: a point, a periodic orbit and a strange attractor

The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. We study using analytic tools the dynamics of such system. We describe its global dynamics at infinity, and show that it has no Darboux first integrals. Additionally, we characterize its Hopf bifurcations

On the polynomial integrability of a system motivated by the Riemann ellipsoid problem

Agraïments: The second author was supported by AGAUR grant PIV-DGR-2010 and by FCT through the project PTDC/MAT/117106/2010 and through CAMGSD, Lisbon.We consider differential systems obtained by coupling two Euler-Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. We also prove that these systems either are completely integrable or have at most four functionally independent analytic first integrals

On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n

Altres ajuts: FEDER-UNAB-10-4E378We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1/2 d∑i=1 p21+V(q1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral

Integrability of reversible and equivariant quadratic polynomial differential systems in the plane

Altres ajuts: ICREA AcademiaWe study the existence of first integrals for the class of reversible and equivariant quadratic polynomial differential systems in the plane. We put special emphasis in the study of the analytic first integrals

Discrete Melnikov functions

We consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented.) having when (Formula presented.) an open continuum of initial conditions such that the corresponding sequences are N-periodic. From the study of some variational equations of low order, we obtain successive maps, that we call discrete Melnikov functions, such that the simple zeroes of the first one that is not identically zero control the initial conditions that persist as N-periodic sequences of the perturbed discrete dynamical system. We apply these results to several examples, including some Abel-type discrete dynamical systems and some non-autonomous perturbed globally periodic difference equations