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.

Shocks, Monetary Policy and Institutions: Explaining Unemployment Persistence in Persistence in “Europe” and the United States

This paper examines the rise in European unemployment since the 1970s by introducing endogenous growth into an otherwise standard New Keynesian model with capital accumulation and unemployment. We subject the model to an uncorrelated cost push shock, in order to mimic a scenario akin to the one faced by central banks at the end of the 1970s. Monetary policy implements a disinfl ation by following an interest feedback rule calibrated to an estimate of a Bundesbank reaction function. 40 quarters after the shock has vanished, unemployment is still about 1.8 percentage points above its steady state. Our model also broadly reproduces cross country differences in unemployment by drawing on cross country differences in the size of cost push shock and the associated disinfl ation, the monetary policy reaction function and the wage setting structure.

Endogenous Price Flexibility and Optimal Monetary Policy

Much of the literature on optimal monetary policy uses models in which the degree of nominal price flexibility is exogenous. There are, however, good reasons to suppose that the degree of price flexibility adjusts endogenously to changes in monetary conditions. This paper extends the standard New Keynesian model to incorporate an endogenous degree of price flexibility. The model shows that endogenising the degree of price flexibility tends to shift optimal monetary policy towards complete inflation stabilisation, even when shocks take the form of cost-push disturbances. This contrasts with the standard result obtained in models with exogenous price flexibility, which show that optimal monetary policy should allow some degree of inflation volatility in order to stabilise the welfarerelevant output gap.

Social Housing Policies in Latin America and Singapore: Lessons for China

This paper addresses the challenges facing China in accelerating the pace of rural-urban migration as part of its on-going economic development programme. It explains the push and pull influences on migration and in particular explains why a continuing focus on urbanisation is justified by the very large gap between rural and urban incomes and the relatively higher income elasticity of demand for urban-based goods and services. The provision of affordable housing is an integral part of this structural shift programme. The paper thus considers the most appropriate ways in which housing finance can be mobilised, and thence how both the quality and the affordability of the housing stock can be increased. Positive and negative lessons for China are offered from the different urbanisation experiences of Latin America (especially Colombia) and Singapore.

How Optimal is US Monetary Policy?

Most of the literature estimating DSGE models for monetary policy analysis assume that policy follows a simple rule. In this paper we allow policy to be described by various forms of optimal policy - commitment, discretion and quasi-commitment. We find that, even after allowing for Markov switching in shock variances, the inflation target and/or rule parameters, the data preferred description of policy is that the US Fed operates under discretion with a marked increase in conservatism after the 1970s. Parameter estimates are similar to those obtained under simple rules, except that the degree of habits is significantly lower and the prevalence of cost-push shocks greater. Moreover, we find that the greatest welfare gains from the ‘Great Moderation’ arose from the reduction in the variances in shocks hitting the economy, rather than increased inflation aversion. However, much of the high inflation of the 1970s could have been avoided had policy makers been able to commit, even without adopting stronger anti-inflation objectives. More recently the Fed appears to have temporarily relaxed policy following the 1987 stock market crash, and has lost, without regaining, its post-Volcker conservatism following the bursting of the dot-com bubble in 2000.

The Inflation Bias under Calvo and Rotemberg Pricing.

New Keynesian models rely heavily on two workhorse models of nominal inertia - price contracts of random duration (Calvo, 1983) and price adjustment costs (Rotemberg, 1982) - to generate a meaningful role for monetary policy. These alternative descriptions of price stickiness are often used interchangeably since, to a first order of approximation they imply an isomorphic Phillips curve and, if the steady-state is efficient, identical objectives for the policy maker and as a result in an LQ framework, the same policy conclusions. In this paper we compute time-consistent optimal monetary policy in bench-mark New Keynesian models containing each form of price stickiness. Using global solution techniques we find that the inflation bias problem under Calvo contracts is significantly greater than under Rotemberg pricing, despite the fact that the former typically significant exhibits far greater welfare costs of inflation. The rates of inflation observed under this policy are non-trivial and suggest that the model can comfortably generate the rates of inflation at which the problematic issues highlighted in the trend inflation literature emerge, as well as the movements in trend inflation emphasized in empirical studies of the evolution of inflation. Finally, we consider the response to cost push shocks across both models and find these can also be significantly different. The choice of which form of nominal inertia to adopt is not innocuous.

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."

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.

Trade liberalization, competition and growth

Increasing evidence support the claim that international trade enhances innovation and productivity growth through an increase in competition. This paper develops a two-country endogenous growth model, with firm specific R&D and a continuum of oligopolistic sectors under Cournot competition to provide a theoretical support to this claim. Since countries are assumed to produce the same set of varieties, trade openness makes markets more competitive, reducing prices and increasing quantities. Under Cournot competition, trade is pro-competitive. Since firms undertake cost reducing innovations, the increase in production induced by a more competitive market push firms to innovate more. Consequently, a reduction on trade barriers enhances growth by reducing domestic firm's market power.

Schistosomiasis control in the State of São Paulo

The program of schistosomiasis control for the State of São Paulo, where only low endemicity areas occur, is discussed in this paper. Inclusion of schistosomiasis among the diseases due to obligatory notification is considered as a measure of great importance. Accordingly the search for passive cases conducted by the public health system acquired major importance in the disease surveillance. As from 1981 to 1992 only 11% of the detected cases were considered as autochthonous. The main transmission areas are located at the Litoral and Paraiba Valley regions. In the period of time under analysis, the epidemiological surveillance data suggest a decrease in the morbidity and in the autochthony tendency in the State of São Paulo.

Abdominal Angiostrongylosis in Southern Brazil - Prevalence and Parasitic Burden in Mollusc Intermediate Hosts from Eighteen Endemic Foci

Angiostrongylus costaricensis is a parasitic nematode of rodents and molluscs are the intermediate hosts. Nocturnal collection of molluscs and search for infective third stage larvae of A. costaricensis was carried out in 18 endemic foci identified by the notification of a confirmed diagnosis in human biopsies or surgical specimens. Molluscs were digested in acidic solution and isolation of larvae eventually present was done in a Baermann funnel. Larvae identified by the presence of a delicate groove in the tail were counted to assess the individual parasitic burden. Four species were found infected, with ranges of prevalence in parenthesis: Phyllocaulis variegatus (7% to 33.3%); Bradybaena similaris (11.7% to 24.1%); Belocaulus angustipes (8.3% ) and Phyllocaulis soleiformis (3.3% to 14.2%). Parasitic burden varied from 1 to 75 with P. variegatus, 1 to 98 with B. similaris, 1 to 13 with B. angustipes and 1 larvae in each of two specimens of P. soleiformis. P. variegatus was present in all sites and was found infected with the highest prevalence figures and the highest individual parasitic burdens. These data stress the importance of veronicellid slugs as intermediate hosts for A. costaricensis in the endemic areas in Rio Grande do Sul, Brazil

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.

Spatial distribution of economic activities: an empirical approach usingself-organizing maps

The aim of this paper is to analyse the colocation patterns of industries and firms. We study the spatial distribution of firms from different industries at a microgeographic level and from this identify the main reasons for this locational behaviour. The empirical application uses data from Mercantile Registers of Spanish firms (manufacturers and services). Inter-sectorial linkages are shown using self-organizing maps. Key words: clusters, microgeographic data, self-organizing maps, firm location JEL classification: R10, R12, R34