Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Strange nonchaotic attractors in Harper maps

We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.

Economic growth and atmospheric pollution in Spain: discussing the environmental Kuznets curve by hypothesis

The environmental Kuznets curve (EKC) hypothesis posits an inverted U relationship between environmental pressure and per capita income. Recent research has examined this hypothesis for different pollutants in different countries. Despite certain empirical evidence shows that some environmental pressures have diminished in developed countries, the hypothesis could not be generalized to the global relationship between economy and environment at all. In this article we contribute to this debate analyzing the trends of annual emission flux of six atmospheric pollutants in Spain. The study presents evidence that there is not any correlation between higher income level and smaller emissions, except for SO2 whose evolution might be compatible with the EKC hypothesis. The authors argue that the relationship between income level and diverse types of emissions depends on many factors. Thus it cannot be thought that economic growth, by itself, will solve environmental problems.

Long-run Inflation-Unemployment Dynamics: The Spanish Phillips Curve and Economic Policy

This paper takes a new look at the long-run dynamics of inflation and unemployment in response to permanent changes in the growth rate of the money supply. We examine the Phillips curve from the perspective of what we call "frictional growth", i.e. the interaction between money growth and nominal frictions. After presenting theoretical models of this phenomenon, we construct an empirical model of the Spanish economy and, in this context, we evaluate the long-run inflation-unemployment trade for Spain and examine how recent policy changes have afected it.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Quasiconformal maps, analytic capacity, and non linear potentials

"Vegeu el resum a l'inici del document del fitxer adjunt."

A doubling measure on R(d) can charge a rectifiable curve

"Vegeu el resum a l'inici del document del fitxer adjunt"

Aplicación con Google Maps

El principal objetivo de este proyecto es realizar un aplicativo web que utilice API’s para que, a partir de un conjunto de rutas almacenadas en el sistema, éste sea capaz de generar nuevas rutas a partir de éstas, de modo que dicho sistema no se comporte como un mero "almacén" de rutas introducidas por los usuarios para poder ser utilizadas por los demás posteriormente, sino que podamos ser nosotros mismos los que decidamos ciertos aspectos de la ruta que deseamos que el sistema nos proporcione. Así, el aplicativo desarrollado, partiendo de un conjunto previo de rutas, será capaz de generar nuevas rutas pasando lo más cerca posible de un conjunto de puntos definidos por el usuario, pudiendo ser calculadas siguiendo diferentes parámetros de optimización tales como el menor número de rutas utilizadas en el cálculo o el menor número de intersecciones entre ellas. Estas rutas, posteriormente, pueden visualizarse en la aplicación mediante el API de Google Maps, o pueden ser descargadas para utilizarlas en nuestro dispositivo GPS portátil.

A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

Inflation dynamics and the New Keynesian Phillips curve in EU-4

The paper seeks to shed light on inflation dynamics of four new EU member states: the Czech Republic, Hungary, Poland and Slovakia. To this end, the New Keynesian Phillips curve augmented for open economies is estimated and additional statistical tests applied. We find the following. (1) The claim of New Keynesians that the real marginal cost is the main inflation-forcing variable is fragile. (2) Inflation seems to be driven by external factors. (3) Although inflation holds a forward-looking component, the backward-looking component is substantial. An intuitive explanation for higher inflation persistence may be rather adaptive than rational price setting of local firms.

Geolocalitzáció en temps real sobre Google Maps

L’objectiu d’aquest projecte és crear un sistema de seguiment d’una flota de vehicles amb GPS en temps real. A partir d’un mòdul de captació, el servidor recull la informació geogràfica dels vehicles i l’emmagatzema. I amb un mòdul de processament, es mostra i controla els vehicles, els punts d’interès i els polígons del sistema de Geofencing. En primer lloc, faig una introducció a l’estat de l’art dels sistemes de seguiment de vehicles. A continuació, analitzo els requeriments, especifico el comportament desitjat del sistema, explico el disseny i la implementació. Per últim, faig un seguit de proves per extreure’n les conclusions.

Reconsideration of dimensions and curve fitting practice in economics ellaborating on Georgescu-Roegen’s economic methodology

This paper is to examine the proper use of dimensions and curve fitting practices elaborating on Georgescu-Roegen’s economic methodology in relation to the three main concerns of his epistemological orientation. Section 2 introduces two critical issues in relation to dimensions and curve fitting practices in economics in view of Georgescu-Roegen’s economic methodology. Section 3 deals with the logarithmic function (ln z) and shows that z must be a dimensionless pure number, otherwise it is nonsensical. Several unfortunate examples of this analytical error are presented including macroeconomic data analysis conducted by a representative figure in this field. Section 4 deals with the standard Cobb-Douglas function. It is shown that the operational meaning cannot be obtained for capital or labor within the Cobb-Douglas function. Section 4 also deals with economists "curve fitting fetishism". Section 5 concludes thispaper with several epistemological issues in relation to dimensions and curve fitting practices in economics.