Browsing by Subject "Differentiable dynamical systems"
Now showing items 2140 of 159

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® ... 
Codimension3 bifurcation for continuous saddle bimodal linear dynamical systems
(20180201)
Article
Open AccessWe continue the study of the structural stability and the bifurcations of planar continuous bimodal linear dynamical systems (that is, systems consisting of two linear dynamics acting on each side of a straight line, ... 
Communication through coherence in a realistic neuronal model
(Universitat Politècnica de Catalunya, 202007)
Master thesis
Open AccessThe Communication Through Coherence (CTC) theory establishes that neural communication is much effective if the underlying oscillatory activity of both populations are phase locked, that is, the input from the emitting ... 
Computation of invariant curves in the analysis of periodically forced neural oscillators
(Springer, 2018)
Part of book or chapter of book
Open AccessBackground 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 ... 
ComputerAssited Proofs in Dynamics
(Universitat Politècnica de Catalunya, 202010)
Master thesis
Restricted access  author's decisionInterval analysis is presented as a solution to obtain rigorous results using computers. We present a methodology of computerassisted proofs which involves the use of interval computations. In this thesis we introduce the ... 
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)
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 ... 
Couplingmediated ghost resonance in mutually injected lasers
(200503)
Article
Restricted access  publisher's policy 
Critical velocity in kink solutions of the sineGordon equation
(Universitat Politècnica de Catalunya, 201707)
Master thesis
Open AccessThe goal of this work is to present a way to deduce the value of the critical velocity observed in solitonlike solutions of a perturbed version of the sineGordon equation. To do so, an ODE system is obtained from the ... 
Darboux integrability and invariant algebraic curves for planar polynomial systems
(2004)
Article
Open AccessIn this paper we study the normal forms of polynomial systems having a set of given generic invariant algebraic curves. 
Detection of Lagrangian Coherent Structures in oceanic flows
(Universitat Politècnica de Catalunya, 202107)
Master thesis
Open AccessThe Atlantic Meridional Overturning Circulation (AMOC) is a complex system of shallow and deep currents in the Atlantic Ocean which plays a crucial role in the regulation of the Earth's climate. Lagrangian Coherent Structures ... 
Different approaches to the global periodicity problem
(20130725)
Research report
Open Accesst Let F be a real or complex ndimensional map. It is said that F is globally periodic if there exists some p ∈ N + such that Fp(x) = x for all x, where F k = F ◦ F k−1, k ≥ 2. The minimal p satisfying this property is ... 
Discrete nonholonomic LL systems on Lie groups
(2003)
Article
Open AccessThis paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic leftinvariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two ...