Publicaciones del CMAT
http://archive.cmat.edu.uy
Publicaciones de los docentes del Centro de Matemática
daily12009-06-03T05:25:56ZMonads on higher monoidal categories http://archive.cmat.edu.uy/docentes/negra/publicaciones/AHL2017 No publishernegra2018-02-01T12:53:14ZArticle ReferenceThe Igusa-Todorov function for comodules http://archive.cmat.edu.uy/docentes/negra/publicaciones/HLM2016 No publishernegra2018-02-01T12:53:23ZArticle ReferenceCondition length and complexity for the solution of polynomial systems http://archive.cmat.edu.uy/docentes/diego/publicaciones/ABB1000 Smale’s 17th problem asks for an algorithm which finds an approximate zero of polynomial systems in average polynomial time (see Smale in Mathematical problems for the next century, American Mathematical Society, Providence, 2000). The main progress on Smale’s problem is Beltrán and Pardo (Found Comput Math 11(1):95–129, 2011) and Bürgisser and Cucker (Ann Math 174(3):1785–1836, 2011). In this paper, we will improve on both approaches and prove an interesting intermediate result on the average value of the condition number. Our main results are Theorem 1 on the complexity of a randomized algorithm which improves the result of Beltrán and Pardo (2011), Theorem 2 on the average of the condition number of polynomial systems which improves the estimate found in Bürgisser and Cucker (2011), and Theorem 3 on the complexity of finding a single zero of polynomial systems. This last theorem is similar to the main result of Bürgisser and Cucker (2011) but relies only on homotopy methods, thus removing the need for the elimination theory methods used in Bürgisser and Cucker (2011). We build on methods developed in Armentano et al. (2014).No publisherdiego2016-09-07T19:38:56ZArticle ReferenceGeneric uniqueness of the minimal Moulton central configuration http://archive.cmat.edu.uy/docentes/emaderna/publicaciones/articlereference.2014-06-27.2684319648 We prove that, for generic (open and dense) values of the masses, the Newtonian potential function of the collinear N-body problem has N!/2 critical values when restricted to a fixed inertia level. In particular, we provee that for generic masses, there is only one minimal Moulton configuration. We give a very short proof of an improved version of classical Moulton's theorem using the Gershgorin circle theorem and a normalization of central configurations introduced by Yoccoz in 1986. Then the proof of the main theorem follows by reduction to the case of three bodies, in which we apply a theorem by Euler of 1765.No publisheremaderna2015-09-29T19:28:29ZArticle ReferenceClassification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group http://archive.cmat.edu.uy/docentes/rpotrie/publicaciones/HP2013a No publisherrpotrie2015-06-06T17:08:36ZArticle ReferenceOn Cremona Transformations of P^3 with all possible bidegree http://archive.cmat.edu.uy/gruposinvestigacion/teoinv/publicaciones/pre-prints/preprintreference.2014-04-03.0940563587 No publishergcorrea2014-04-03T20:45:05ZPreprint ReferenceReductive an unipotent actions of algebraic groups http://archive.cmat.edu.uy/gruposinvestigacion/teoinv/publicaciones/pre-prints/preprintreference.2014-04-03.9959235281 No publishergcorrea2014-04-03T20:45:04ZPreprint ReferenceSystems of polynomial equations defining hyperelliptic d-osculating covers http://archive.cmat.edu.uy/gruposinvestigacion/teoinv/publicaciones/articulos/articlereference.2014-04-06.2875436774 No publisheralvaro2014-05-04T20:34:25ZArticle ReferenceHyperelliptic d-osculating covers and rational surfaces http://archive.cmat.edu.uy/gruposinvestigacion/teoinv/publicaciones/articulos/articlereference.2014-04-06.0715107243 No publisheralvaro2014-05-04T20:33:20ZArticle ReferenceMorita equivalence of partial group actions and globalization http://archive.cmat.edu.uy/gruposinvestigacion/teoinv/publicaciones/articulos/articlereference.2014-04-06.2185380020 No publisheralvaro2014-05-04T20:29:18ZArticle ReferenceThe Endomorphisms Monoid of a Homogenous Vector Bundle http://archive.cmat.edu.uy/gruposinvestigacion/teoinv/publicaciones/articulos/articlereference.2014-04-03.7616950258 In this paper we give some properties of the algebraic and geometric structure of the endomorphisms monoid of a homogeneous vector bundle.No publishergcorrea2014-05-04T20:30:48ZArticle ReferenceOn the free time minimizers of the Newtonian N-body problem http://archive.cmat.edu.uy/docentes/emaderna/publicaciones/articlereference.2010-10-19.5734136585 The Hamiltonian formulation of the Newtonian N-body problem assures that motions are characterized by the local minimization property of the Lagrangian action. In this paper we study the dynamics of a very special class of motions, which satisfy a strong global minimization property. More precisely, we call a free time minimizer a curve which satisfies the least action principle between any pair of its points without the constraint of time for the variations. A simple example of a free time minimizer defined on an unbounded interval is a parabolic homothetic motion by a minimal central configuration. The existence of a large amount of free time minimizers can be deduced from the weak KAM theorem. In particular, for any choice of y in E^N , there should be at least one free time minimizer x on [0,+∞) which satisfies x(0)=y. We prove that such motions are completely parabolic meaning that the velocity of each body goes to zero as t goes to +∞. More precisely, we show that the energy of that motions is zero, that the moment of inertia grows like t^{4/3}, and that the potential energy decay is like t^{-2/3}. Using Marchal's theorem, which states that minimizers avoid collisions we can deduce as a corollary that there are no complete free time minimizers, i.e. defined on (-∞,+∞).No publisheremaderna2014-02-06T17:12:08ZArticle ReferenceA few remarks on partially hyperbolic diffeomorphisms of T^3 isotopic to Anosov http://archive.cmat.edu.uy/docentes/rpotrie/publicaciones/Pot2013a No publisherrpotrie2014-07-25T01:56:01ZArticle ReferencePointwise partial hyperbolicity in 3-dimensional nilmanifolds http://archive.cmat.edu.uy/docentes/rpotrie/publicaciones/HP2013 No publisherrpotrie2014-07-25T01:53:53ZArticle ReferencePartial hyperbolicity and foliations in T^3 http://archive.cmat.edu.uy/docentes/rpotrie/publicaciones/Pot2012 No publisherrpotrie2014-07-25T01:51:04ZArticle Reference