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.

Strongly non-degenerate Lie algebras

Let A be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra Der(A) of(associative) derivations of A is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of A. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra A with involution and the Lie algebra SDer(A) of involution preserving derivations of A

The EU as a security provider in its neighbourhood: the case of non-proliferation of WMD in the Mediterranean area

As a consequence of the terrorist attacks of 9/11 and the US-led war against Iraq, WMD and their proliferation have become a central element of the EU security agenda. In December 2003, the European Council adopted even a EU Strategy against Proliferation of WMD. The approach adopted in this Strategy can be largely described as a ‘cooperative security provider’ approach and is based on effective multilateralism, the promotion of a stable international and regional environment and the cooperation with key partners. The principal objective of this paper is to examine in how far the EU has actually implemented the ‘cooperative security provider’ approach in the area which the Non-proliferation Strategy identifies as one of its priorities – the Mediterranean. Focusing on the concept of security interdependence, the paper analyses first the various WMD dangers with which the EU is confronted in the Mediterranean area. Afterwards, it examines how the EU has responded to these hazards in the framework of the Barcelona process and, in particular, the new European Neighbourhood Policy. It is argued that despite its relatively powerful rhetoric, the EU has largely failed, for a wide range of reasons, to apply effectively its non-proliferation approach in the Mediterranean area and, thus, to become a successful security provider.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

Contraction groups in complete Kac-Moody groups

Let G be an abstract Kac-Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

Wealth constraints, skill prices or networks: what determines emigrant selection?

The productive characteristics of migrating individuals, emigrant selection, affect welfare. The empirical estimation of the degree of selection suffers from a lack of complete and nationally representative data. This paper uses a new and better dataset to address both issues: the ENET (Mexican Labor Survey), which identifies emigrants right before they leave and allows a direct comparison to non-migrants. This dataset presents a relevant dichotomy: it shows on average negative selection for Mexican emigrants to the United States for the period 2000-2004 together with positive selection in Mexican emigration out of rural Mexico to the United States in the same period. Three theories that could explain this dichotomy are tested. Whereas higher skill prices in Mexico than in the US are enough to explain negative selection in urban Mexico, its combination with network effects and wealth constraints is required to account for positive selection in rural Mexico.

In Search of a theory of debt management

A growing literature integrates theories of debt management into models of optimal fiscal policy. One promising theory argues that the composition of government debt should be chosen so that fluctuations in the market value of debt offset changes in expected future deficits. This complete market approach to debt management is valid even when the government only issues non-contingent bonds. A number of authors conclude from this approach that governments should issue long term debt and invest in short term assets. We argue that the conclusions of this approach are too fragile to serve as a basis for policy recommendations. This is because bonds at different maturities have highly correlated returns, causing the determination of the optimal portfolio to be ill-conditioned. To make this point concrete we examine the implications of this approach to debt management in various models, both analytically and using numerical methods calibrated to the US economy. We find the complete market approach recommends asset positions which are huge multiples of GDP. Introducing persistent shocks or capital accumulation only worsens this problem. Increasing the volatility of interest rates through habits partly reduces the size of these simulations we find no presumption that governments should issue long term debt ? policy recommendations can be easily reversed through small perturbations in the specification of shocks or small variations in the maturity of bonds issued. We further extend the literature by removing the assumption that governments every period costlessly repurchase all outstanding debt. This exacerbates the size of the required positions, worsens their volatility and in some cases produces instability in debt holdings. We conclude that it is very difficult to insulate fiscal policy from shocks by using the complete markets approach to debt management. Given the limited variability of the yield curve using maturities is a poor way to substitute for state contingent debt. The result is the positions recommended by this approach conflict with a number of features that we believe are important in making bond markets incomplete e.g allowing for transaction costs, liquidity effects, etc.. Until these features are all fully incorporated we remain in search of a theory of debt management capable of providing robust policy insights.