Expansiveness, Lyapunov exponents and entropy for set valued maps

In this paper we introduce a notion of expansiveness for a set valued map defined on a topological space different from that given by Richard Williams at \cite{Wi, Wi2} and prove that the topological entropy of an expansive set valued map defined on a Peano space of positive dimension is greater than zero. We define Lyapunov exponent for set valued maps and prove that positiveness of its Lyapunov exponent implies positiveness for the topological entropy. Finally we introduce the definition of (Lyapunov) stable points for set valued maps and prove a dichotomy for the set of stable points for set valued maps defined on Peano spaces: either it is empty or the whole space.Comment: 24 pages, 1 figur

N-expansive homeomorphisms on surfaces

We exploit the techniques developed in [Le] to study N-expansive homeomorphisms on surfaces. We prove that when f is a 2-expansive homeomorphism defined on a compact boundaryless surface M without wandering points then f is expansive. This condition on the wandering set cannot be relaxed: we present an example of a 2-expansive homeomorphisms on the bitorus with wandering points that is not expansive

Regional arrangements to support growth and macro-policy coordination in MERCOSUR

The main goal of the paper is to discuss the problem of macroeconomic policy coordination in MERCOSUR and how it could contribute to sustaining growth. In the first part, the paper reviews the macroeconomic situation of MERCOSUR, emphasizing the role of the developments that followed the regime change in Brazil in 1999 and in other member countries afterwards. The analysis suggests that the worst consequences of the crises have been overcome and MERCOSUR will probably enter a new stage in which intra-regional trade will resume the positive trend that it showed before the crises. However, for this new stage to consolidate, it is crucial that Brazil increases its growth rate significantly. The second part analyses the characteristics of macroeconomic fluctuations in the region. The paper focuses on three dimensions that are key to designing a framework for macroeconomic policy coordination. The first is cyclical movements within countries and the co-movements between MERCOSUR members. The study allows us to distinguish between the effects of common (i.e. regional) and idiosyncratic shocks. The second dimension is price and quantity dynamics and the interactions between the activity level and the real exchange rate. The third has to do with those financial market failures that contribute to creating and amplifying the shocks that impinge on the region. The last section addresses what member countries can do to support growth, macro-policy coordination, and financial integration. It is suggested that for macroeconomic coordination to progress, it is crucial to identify how the incentives to coordinate can be strengthened in order to avoid coordination failures that are similar to those that followed the post-1999 crises and that had a deleterious effect on intra-regional trade. From the study of cyclical movements, prices and financial failures, it follows that the strategy for the implementation of the coordination framework should be able to work under conditions of excess volatility; must take into account that the international financial architecture is far from developing-country friendly; and, must emphasize the role of institution-building at the regional level.

Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators

This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For $L$ in some class of elliptic operators, we study weighted norm $L^p$ inequalities for singular 'non-integral' operators arising from $L$ ; those are the operators $\phi(L)$ for bounded holomorphic functions $\phi$, the Riesz transforms $\nabla L^{-1/2}$ (or $(-\Delta)^{1/2}L^{-1/2}$) and its inverse $L^{1/2}(-\Delta)^{-1/2}$, some quadratic functionals $g\_{L}$ and $G\_{L}$ of Littlewood-Paley-Stein type and also some vector-valued inequalities such as the ones involved for maximal $L^p$-regularity. For each, we obtain sharp or nearly sharp ranges of $p$ using the general theory for boundedness of Part I and the off-diagonal estimates of Part II. We also obtain commutator results with BMO functions.Comment: 38 pages. Third of 4 paper

Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part II: Off-diagonal estimates on spaces of homogeneous type

This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a measure of decay. This substitute is that of off-diagonal estimates expressed in terms of local and scale invariant $L^p-L^q$ estimates. We propose a definition in spaces of homogeneous type that is stable under composition. It is particularly well suited to semigroups. We study the case of semigroups generated by elliptic operators.Comment: 40 pages. Second of 4 papers. Can be read independentl

Weighted norm inequalities for fractional operators]

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-$\lambda$ method that does not use any size or smoothness estimates for the kernels.Comment: accepted in Indiana University Mathematicla Journal. A thorough reorganisation has been done on suggestions from the refere

On the Use of the First Principal Component as a Core Inflation Indicator

This paper investigates if the (OLS-scaled) first principal component (PC1), extracted from standardized yearly rates of change of basic items of the CPI, represents a reasonable option for a core inflation indicator. The evaluation is carried out by (i) confronting alternative linear transformations of the original variables; (ii) analyzing the impact of stacking lagged variables to the original database; and (iii) exploring the contents of the remaining principal components. An orthogonal factor model framework will also be introduced so as to fully reproduce any variable that can be expressed as a linear combination of the original input variables, such as, in this case, the overall inflation rate. The model incorporates the following properties: (i) the results are not conditional on the eigenvectors length; (ii) the variance of the CPI accounted for by each component is unique, and (iii) the outcome is equivalent to an OLS regression between the CPI and the PC1. Along with empirical evidence for the Portuguese case, it will be claimed that the above-mentioned (OLS-scaled) PC1 does capture the general movement of the overall inflation rate, however, no OLS regression would have to be implemented if the core indicator is fully aligned with the orthogonal factor model.