Browsing by Subject "Sistemes dinàmics diferenciables"
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Asymptotic size of Herman Rings using quasiconformal surgery
(Universitat Politècnica de Catalunya, 201607)
Bachelor thesis
Open AccessThis thesis gives an introduction to the theory of quasiconformal surgery. To that end, we consider the complexification of the Arnol'd standard family of circle maps. These functions are analytically linearisable under ... 
A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems
(20170901)
Article
Open AccessPiecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should the dynamics be given ... 
AutoBacklund transformations and special integrals for differentialdelay Painlevé hierarchies
(20141001)
Article
Restricted access  publisher's policyThe six Painleve equations have attracted much interest over the last thirty years or so. More recently many authors have begun to explore properties of higherorder versions of both these equations and their discrete ... 
Biasymptotic billiard orbits inside perturbed ellipsoids
(2001)
Article
Open Access 
Bigbang bifurcations in a first order system with a relay
(2011)
Conference report
Restricted access  publisher's policyIn this work we describe the bifurcation scenario found in a general first order system when a relay based proportional control is considered. We show the existence of a big bang bifurcation causing the existence of an ... 
Breakdown of a 2D heteroclinic connection in the hopfzero singularity (I)
(20181001)
Article
Open AccessIn this paper we study a beyond all orders phenomenon which appears in the analytic unfoldings of the Hopfzero singularity. It consists in the breakdown of a twodimensional heteroclinic surface which exists in the truncated ... 
Breakdown of a 2D heteroclinic connection in the Hopfzero singularity (II): The generic case
(20180417)
Article
Open AccessIn this paper, we prove the breakdown of the twodimensional stable and unstable manifolds associated to two saddlefocus points which appear in the unfoldings of the Hopfzero singularity. The method consists in obtaining ... 
Chaos in the hysteretic grazingsliding codimensionone saddlenode bifurcation of piecewise dynamical systems
(UP4, Institute of Sciences, S.L., 2017)
Conference lecture
Open AccessWe present two ways of regularizing a parameter family of piecewise smooth dynamical systems undergoing a grazing sliding bifurcation. We use the SotomayorTeixeira regularization and prove that the bifurcation is a ... 
Chaotic advection, transport and patchiness in clouds of pollution in an estuarine flow
(American Institute of Mathematical Sciences, 2001)
Article
Open AccessWe present an application of the transport theory developed for area preserving dynamical systems, to the problem of pollution and in particular patchiness in clouds of pollution in partially stratified estuaries. We ... 
Chaotic dynamics of the Kepler problem with variable gravitational coefficient
(Universitat Politècnica de Catalunya, 201707)
Master thesis
Open AccessOn this work we prove the presence of chaotic dynamics for the classical twobody Kepler problem with a timeperiodic variable gravitational coefficient using two different methods, the stretching along the path (SAP) ... 
Closed Geodesics and Billiards on Quadrics related to elliptic KdV solutions
(2004)
Article
Open AccessWe consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkho® ... 
Computation of invariant curves in the analysis of periodically forced neural oscillators
(Springer, 2018)
Part of book or chapter of book
Restricted access  publisher's policyBackground oscillations, reflecting the excitability of neurons, are ubiq uitous in the brain. Some studies have conjectured that when spikes sent by one population reach the other population in the peaks of excitability, ... 
Computation of periodic orbits and their invariant manifolds in the RTBP
(Universitat Politècnica de Catalunya, 201407)
Master thesis
Open AccessThis project is a study of the RTBP, in particular of a modification of this problem devised to study orbits of the Moon. Some parts of the project are done analytically while others numerically. The analytical part focuses ... 
Computation of the invariant manifolds of infinity in the restricted circular planar three body problem with the parametrization method
(Universitat Politècnica de Catalunya, 201705)
Master thesis
Open AccessThis work analyses the parabolic stable manifolds of the periodic orbits at infinity for the Restricted Planar Circular Three Body Problem. Using the parametrization method we prove the existence of such manifold and we ... 
Constraint algorithm for extremals in optimal control problems
(20070727)
Article
Open AccessA characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of ... 
Constraint algorithm for kpresymplectic Hamiltonian systems. Application to singular field theories
(20090310)
Working paper
Open AccessThe ksymplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic ... 
Continua of periodic points for planar integrable rational maps
(Research India Publications, 201609)
Article
Open AccessWe present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used by other authors and apply ... 
Continua of periodic points for planar integrable rational maps.
(20151130)
External research report
Open AccessWe present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used for other authors and apply ... 
Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
(201409)
External research report
Open AccessWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearlyintegrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider ... 
Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
(Springer, 201411)
Article
Open AccessWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We ...