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In this paper we introduce two definitions of upper porosity of a measure which range from 0 to (1/2) and from 0 to 1 respectively, and prove that actually the first porosity only can take the extreme values 0 or (1/2), and the second one takes [...]texto impreso
We analyze the convergence conditions of the Eckmann and Ruelle algorithm (E.R.A. for the sequel) used to estimate the Liapunov exponents, for the tangent map, of an ergodic measure, invariant under a smooth dynamical system. We find sufficient [...]texto impreso
Vázquez Furelos, Mercedes ; Herrera de la Cruz, Jorge ; Mera Rivas, María Eugenia ; Rodrigo Fernández, Antonio ; Moreta Santos, Mª Jesús ; Lugo Arocha, Haydee Corina ; García Pineda, Mª Pilar ; López Zorzano, Rafael Alberto ; Dueñas Ballesteros, Juan Manuel ; Alonso González, Alvaro | 2019-06-14En este informe se detalla el contenido del curso propedéutico de Matemáticas Básicas para la facultad de Ciencias Económicas y Empresariales, así como los resultados de la impartición en modalidad semi-presencial como novedad.texto impreso
We give a formal proof that if f is a smooth dynamics on a d-dimensional smooth manifold and ? is an ergodic and exact dimensional measure with Hausdorff dimension dim?> d-1, then the number d of degrees of freedom of the dynamics can be recover[...]texto impreso
Mera Rivas, María Eugenia ; Rey Simo, José Manuel ; Morán Cabré, Manuel | Facultad de Ciencias Económicas y Empresariales. Decanato | 1995En esta memoria se revisan tres herramientas complementarias para el Análisis No-Lineal de Series Temporales: dimensión fractal, entropía, y exponentes de Liapunov. Se hace una revisión crítica del estado de la cuestión en el área, señalando el [...]texto impreso
We estimate the covariance matrix of the errors in several dynamically coupled time series corrupted by measurement errors. We say that several scalar time series are dynamically coupled if they record the values of measurements of the state var[...]texto impreso
We propose an algorithm for the reduction of observational noise in chaotic multivariate time series. The algorithm is based on a maximum likelihood criterion, and its goal is to reduce the mean distance of the points of the cleaned time series [...]texto impreso
We analyze under what conditions the best Lp(?)-linear fittings of the action of a mapping f on small balls give reliable estimates of the tangent map Df. We show that there is an inverse relationship between the conditions on the regularity, in[...]texto impreso
We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. We show that much of the information lost due to measurement noise in a target t[...]texto impreso
LLorente Comí, Marta ; Mera Rivas, María Eugenia ; Morán Cabré, Manuel | Institute of Physics Publishing | 2018We show that the s-dimensional packing measure P^{s}(S) of the Sierpinski gasket S, where s=((log3)/(log2)) is the similarity dimension of S, satisfies 1.6677?P^{s}(S)?1.6713. We present a formula (see Theorem 6) that enables the achievement of [...]texto impreso
Mera Rivas, María Eugenia ; Morán Cabré, Manuel ; Preiss, David ; Zajicek, Ludik | American Physical Society | 2003We show that given a ?-finite Borel regular measure ? in a metric space X, every ?-porous subset of X of finite measure can be approximated by strongly porous sets. It follows that every ?-porous set is the union of a ?-strongly porous set and a[...]texto impreso
Vázquez Furelos, Mercedes ; Herrera de la Cruz, Jorge ; Arenas Amorós, Jorge ; Dueñas Ballesteros, Juan Manuel ; García Pineda, María Pilar ; Gonzalez Vega, Jorge ; López Zorzano, Rafael Alberto ; Lozano Mena, Francisca ; Lugo Arocha, Haydee Corina ; Mera Rivas, María Eugenia ; Rodrigo Fernández, Antonio ; Serrejón Beltran, Francisco Javier ; Vila Rodríguez, Andrés ; Moreta Santos, María Jesus | 2020-06-23En este informe se detalla el funcionamiento del curso semipresencial "Matemáticas G0" que se imparte en todas las titulaciones de la facultad de Ciencias Económicas y Empresariales. Se explora la eficacia de los métodos docentes audiovisuales y[...]texto impreso
In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an automatic computation of the centered Hausdorff and packing measures of a totally disconnected self-similar set. We evaluate these rates empirically[...]texto impreso
We propose a noise reduction algorithm based on adaptive neighbourhood selection able to obtain high levels of noise reduction for chaotic vector time series corrupted by observational noises with a noise to signal ratio of up to 300%.texto impreso
Bujosa Brun, Marcos ; Álvarez González, Francisco ; Barge Gil, Andrés ; Cerdá, Emilio ; Dominguez Toribio, Manuel ; García Hiernaux, Alfredo ; Jerez Méndez, Miguel ; Jiménez Martín, Juan Ángel ; López Zorzano, Rafael Alberto ; Lugo Arocha, Haydee ; Mera Rivas, María Eugenia ; Moreta Santos, María Jesus ; Pérez-Amaral, Teodosio ; Robles Fernández, María Dolores ; Ruiz Andújar, Jesús ; Serrano García, Gregorio ; Sotoca López, Sonia ; Vázquez Furelos, Mercedes | 2015Los exámenes y pruebas de evaluación tienen un papel destacado dentro de los materiales docentes. Ello es así debido al doble papel que juegan: por una parte, son cruciales para evaluar el nivel de conocimientos adquiridos por los estudiantes; p[...]
