75,233 research outputs found
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 in some
class of elliptic operators, we study weighted norm inequalities for
singular 'non-integral' operators arising from ; those are the operators
for bounded holomorphic functions , the Riesz transforms
(or ) and its inverse
, some quadratic functionals and of
Littlewood-Paley-Stein type and also some vector-valued inequalities such as
the ones involved for maximal -regularity. For each, we obtain sharp or
nearly sharp ranges of 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 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- 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.
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