Browsing by Author "MartínezSeara Alonso, M. Teresa"

Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
Bonet Revés, Carles; Sauzin, D.; MartínezSeara Alonso, M. Teresa; València Guitart, Marta (1997)
Article
Open AccessThe linear oscillator equation with a frequency depending slowly on time is used to test a method to compute exponentially small quantities. This work present the matching method in the complex plane as a tool to obtain ... 
A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of T<sup>2</sup>
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (1999)
Article
Open AccessWe give a proof based in geometric perturbation theory of a result proved by J.N. Mather using variational methods. Namely, the existence of orbits with unbounded energy in perturbations of a generic geodesic flow in T^2 ... 
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (2003)
Article
Open AccessWe present a geometric mechanism for diﬀusion in Hamiltonian systems. We also present tools that allow to verify it in a concrete model. In particular, we verify it in a system which presents the large gap problem. 
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model.
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (2003)
Article
Open AccessWe introduce a geometric mechanism for di?usion in a priori unstable nearly integrable dynamical systems. It is based on the observation that resonances, besides destroying the primary KAM tori, create secondary tori and ... 
An analytical approach to codimension2 sliding bifurcations in the dry friction oscillator
MartínezSeara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Hogan, S. John (2010)
Article
Restricted access  publisher's policyIn this paper, we analytically consider sliding bifurcations of periodic orbits in the dryfriction oscillator. The system depends on two parameters: F, which corresponds to the intensity of the friction, and ω, the ... 
Asymptotic behaviour of the domain of analyticity of invariant curves of the standard map
MartínezSeara Alonso, M. Teresa; Villanueva Castelltort, Jordi (1999)
Article
Open AccessIn this paper we consider the standard map, and we study the invariant curve obtained by analytical continuation, with respect to the perturbative parameter E, of the invariant circle of rotation number the golden mean ... 
Asymptotic size of Herman rings of the complex standard family by quantitative quasiconformal surgery
Fagella Rabionet, Núria; MartínezSeara Alonso, M. Teresa; Villanueva Castelltort, Jordi (2003)
Article
Open AccessIn this paper we consider the complexification of the Arnold standard family of circle maps given by $\widetilde F_{\alpha,\ep}(u)=u{\rm e}^{{\rm i}\alpha} {\rm e}^{\frac{\ep}{2}(u\frac{1}{u})}$, with $\alpha=\alpha( ... 
A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems
Bonet Revés, Carles; MartínezSeara Alonso, M. Teresa; Fossas Colet, Enric; Jeffrey, Mike R. (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 ... 
Breakdown of a 2D heteroclinic connection in the hopfzero singularity (I)
Baldomá Barraca, Inmaculada; Castejón Company, Oriol; MartínezSeara Alonso, M. Teresa (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
Baldomá Barraca, Inmaculada; Castejón Company, Oriol; MartínezSeara Alonso, M. Teresa (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 ... 
Breakdown of heteroclinic orbits for analytic unfoldings of the hopfzero singularity. The singular case
Baldomá Barraca, Inmaculada; Castejón i Company, Oriol; MartínezSeara Alonso, M. Teresa (2011)
External research report
Open AccessIn this paper we prove the breakdown of an heteroclinic connection in the analytic versal unfoldings of the generic HopfZero singularity. This heteroclinic orbit appears at any order if one performs the normal form around ... 
Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopfzero singularity
Baldomá Barraca, Inmaculada; MartínezSeara Alonso, M. Teresa (2004)
Article
Open AccessIn this paper we study the exponentially small splitting of a heteroclinic orbit in some unfoldings of the central singularity also called Hopfzero singularity. The fields under consideration are of the form: dx dτ = ... 
Cálculos numéricos de la Hopf zero
Larreal Barreto, Oswaldo José; MartínezSeara Alonso, M. Teresa (2009)
Conference lecture
Open AccessConsideramos la siguiente familia de campos X en R3 : dx dt = − xz − y( + c z) + p+1f( x, y, z, ) dy dt = − yz + x( + c z) + p+1g( x, y, z, ) dz dt = (−1 + b(x2 + y2) + z2) + p+1h( x, y, z, ... 
Chaos in the hysteretic grazingsliding codimensionone saddlenode bifurcation of piecewise dynamical systems
Bonet Revés, Carles; MartínezSeara Alonso, M. Teresa (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 ... 
Computation of invariant curves in the analysis of periodically forced neural oscillators
Pérez Cervera, Alberto; Huguet Casades, Gemma; MartínezSeara Alonso, M. Teresa (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, ... 
Exponentially and nonexponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
Guàrdia Munarriz, Marcel; MartínezSeara Alonso, M. Teresa (201107)
External research report
Open AccessIn this paper we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian System of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables ... 
Exponentially Small Heteroclinic Breakdown in the Generic HopfZero Singularity
Baldomá Barraca, Inmaculada; Castejón i Company, Oriol; MartínezSeara Alonso, M. Teresa (2013)
Article
Restricted access  publisher's policyIn this paper we prove the breakdown of a heteroclinic connection in the analytic versal unfoldings of the generic Hopfzero singularity in an open set of the parameter space. This heteroclinic orbit appears at any order ... 
Exponentially small splitting for the pendulum: a classical problem revisited
MartínezSeara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Olivé, Carme (2010)
Article
Restricted access  publisher's policyIn this paper, we study the classical problem of the exponentially small splitting of separatrices of the rapidly forced pendulum. Firstly, we give an asymptotic formula for the distance between the perturbed invariant ... 
Exponentially small splitting for whiskered tori in Hamiltonian systems: Flowbox coordinates and upper bounds
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere; MartínezSeara Alonso, M. Teresa (2003)
Article
Open AccessWe consider a singular or weakly hyperbolic Hamiltonian, with $n+1$ degrees of freedom, as a model for the behaviour of a nearlyintegrable Hamiltonian near a simple resonance. The model consists of an integrable Hamiltonian ... 
Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results
Baldomá Barraca, Inmaculada; Fontich, Ernest; Guàrdia Munarriz, Marcel; MartínezSeara Alonso, M. Teresa (2011)
External research report
Open AccessIn this paper we study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a nonautonomous perturbation which is fast and periodic in time. We provide ...