Stability and asymptotic analysis of a fluid-particle interaction model

We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov-Fokker-Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.

On dictatorship, economic development and stability

This paper aims to account for varying economic performances and political stability under dictatorship. We argue that economic welfare and social order are the contemporary relevant factors of political regimes' stability. Societies with low natural level of social order tend to tolerate predatory behavior from dictators in exchange of a provision of civil peace. The fear of anarchy may explain why populations are locked in the worst dictatorships. In contrast, in societies enjoying a relative natural civil peace, dictatorship is less likely to be predatory because low economic welfare may destabilize it.

Paths to stability for matching markets with couples

We study two-sided matching markets with couples and show that for a natural preference domain for couples, the domain of weakly responsive preferences, stable outcomes can always be reached by means of decentralized decision making. Starting from an arbitrary matching, we construct a path of matchings obtained from `satisfying' blocking coalitions that yields a stable matching. Hence, we establish a generalization of Roth and Vande Vate's (1990) result on path convergence to stability for decentralized singles markets. Furthermore, we show that when stable matchings exist, but preferences are not weakly responsive, for some initial matchings there may not exist any path obtained from `satisfying' blocking coalitions that yields a stable matching.

Candidate stability and voting correspondences

We study the incentives of candidates to enter or to exit elections in order to strategically affect the outcome of a voting correspondence. We extend the results of Dutta, Jackson and Le Breton (2000), who only considered single-valued voting procedures by admitting that the outcomes of voting may consist of sets of candidates. We show that, if candidates form their preferences over sets according to Expected Utility Theory and Bayesian updating, every unanimous and non dictatorial voting correspondence violates candidate stability. When candidates are restricted to use even chance prior distributions, only dictatorial or bidictatorial rules are unanimous and candidate stable. We also analyze the implications of using other extension criteria to define candidate stability that open the door to positive results.

On the stability of cooperation structures

Qin [J. Eco. Th., 1996] recently showed that in a game of endogenous formation of cooperation structure, if the underlying TU-game is superadditive, then the full cooperation structure is stable. In this note, we characterize the class of games that ensure the stability of the full cooperation structure, and show that this class is much larger than that of superadditive TU-games.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Stability and manipulation in representative democracies

This paper is devoted to the analysis of all constitutions equipped with electoral systems involving two step procedures. First, one candidate is elected in every jurisdiction by the electors in that jurisdiction, according to some aggregation procedure. Second, another aggregation procedure collects the names of the jurisdictional winners in order to designate the final winner. It appears that whenever individuals are allowed to change jurisdiction when casting their ballot, they are able to manipulate the result of the election except in very few cases. When imposing a paretian condition on every jurisdictions voting rule, it is shown that, in the case of any finite number of candidates, any two steps voting rule that is not manipulable by movement of the electors necessarily gives to every voter the power of overruling the unanimity on its own. A characterization of the set of these rules is next provided in the case of two candidates.

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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

On the stability of periodic orbits in Rn

We consider an autonomous differential system in Rn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n ¡ 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

On stability of solutions to systems of convex inequalities

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

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

A non-possibility theorem for joint-stability in interindustry models

Joint-stability in interindustry models relates to the mutual simultaneous consistency of the demand-driven and supply-driven models of Leontief and Ghosh, respectively. Previous work has claimed joint-stability to be an acceptable assumption from the empirical viewpoint, provided only small changes in exogenous variables are considered. We show in this note, however, that the issue has deeper theoretical roots and offer an analytical demonstration that shows the impossibility of consistency between demand-driven and supply-driven models.

The effects of uncertainty about countries' compliance with the Stability and Growth Pact

The Stability and Growth Pact (SGP) was established to govern discretionary fiscal policy in the European Monetary Union. This article studies the effects created when there is uncertainty about the members’ commitment to respecting the established deficit limits in the SGP. We will show that, even if countries respect the SGP deficit ceiling, the presence of uncertainty about their compliance will bring about higher volatility in key economic variables, which could, in turn, affect unemployment and growth negatively. This finding shows that it is important to reduce uncertainty about the members’ commitment towards the SGP. Keywords: fiscal policy rules, monetary union, Stability and Growth Pact, uncertainty, commitment. JEL No.: E63, F55, H62, H87