La seva activitat de recerca està dirigida al desenvolupament de mètodes analítics i numèrics per sistemes dinàmics, gaudint de lideratge científic en diversos temes, com la integrabilitat, els objectes invariants, la teoria K.A.M. (Kolmogorov-Arnold-Moser), els camps vectorials plans i les aplicacions a neurociència, mètode de Poincaré-Melnikov, escissió exponencialment petita de separatrius, difusió, mecànica celest i astrodinàmica.
La qualitat d'aquesta activitat es reflecteix tant en la qualitat i quantitat de publicacions, algunes d'elles en col·laboració amb grups internacionals de primera línia, com en la gestió científica desenvolupada, plasmada en l'organització de múltiples esdeveniments (congressos i jornades , programes de recerca, xarxes temàtiques, etc.), la participació en diversos comitès editorials de revistes de prestigi reconegut, així com en una àmplia formació doctoral.

Su actividad de investigación está dirigida al desarrollo de métodos analíticos y numéricos para sistemas dinámicos, disfrutando de liderazgo científico en diversos temas, como la integrabilidad, los objetos invariantes, la teoría K.A.M. (Kolmogorov-Arnold-Moser), los campos vectoriales planos y las aplicaciones a neurociencia, método de Poincaré-Melnikov, escisión exponencialmente pequeña de separatrices, difusión, mecánica celeste y astrodinámica.
La calidad de esta actividad se refleja tanto en la calidad y cantidad de publicaciones, algunas de ellas en colaboración con grupos internacionales de primera línea, como en la gestión científica desarrollada, plasmada en la organización de múltiples eventos (congresos y jornadas, programas de investigación, redes temáticas, etc.), la participación en diversos comités editoriales de revistas de prestigio reconocido, así como en una amplia formación doctoral.

The UPC dynamical systems group is composed by 20 full time doctors and 3 predocs.

Its research activity is addressed to the development of analytical and numerical methods
for dynamical systems, holding a scientific leading position in several subjects, namely integrability,
invariant objects, KAM theory, planar vector fields and applications to neuroscience, Poincaré-Melnikov
method, exponentially small splitting of separatrices, non-smooth systems, celestial mechanics and astrodynamics.

The quality of this activity is reflected in the quantity and quality of the publications, some of them in
collaboration with cutting edge international research groups as well as in scientific management, leading
to the organization of several events (conferences and meetings, research programs, themed networks, etc),
the participation in several editorial boards of highly regarded journals and a large number of doctoral students.

The UPC dynamical systems group is composed by 20 full time doctors and 3 predocs.

Its research activity is addressed to the development of analytical and numerical methods
for dynamical systems, holding a scientific leading position in several subjects, namely integrability,
invariant objects, KAM theory, planar vector fields and applications to neuroscience, Poincaré-Melnikov
method, exponentially small splitting of separatrices, non-smooth systems, celestial mechanics and astrodynamics.

The quality of this activity is reflected in the quantity and quality of the publications, some of them in
collaboration with cutting edge international research groups as well as in scientific management, leading
to the organization of several events (conferences and meetings, research programs, themed networks, etc),
the participation in several editorial boards of highly regarded journals and a large number of doctoral students.

Recent Submissions

  • A general mechanism of diffusion in hamiltonian systems: qualitative results 

    Gidea, Marian; Llave Canosa, Rafael de la; Martínez-Seara Alonso, M. Teresa (2019-01-01)
    Article
    Open Access
    We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach is based on following the “outer dynamics” along homoclinic orbits to a ...
  • The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability 

    Pérez Cervera, Alberto; Ashwin, Peter; Huguet Casades, Gemma; Rankin, James; Martínez-Seara Alonso, M. Teresa (2019-12-01)
    Article
    Open Access
    We study the dynamics arising when two identical oscillators are coupled near a Hopfbifurcation where we assume a parameter uncouples the system at = 0. Using anormal form forN= 2 identical systems undergoing Hopf bifurcation, ...
  • Hopf-Zero singularities truly unfold chaos 

    Baldomá Barraca, Inmaculada; Ibáñez Mesa, Santiago; Martínez-Seara Alonso, M. Teresa (2020-05-01)
    Article
    Restricted access - publisher's policy
    We provide conditions to guarantee the occurrence of Shilnikov bifurcations in analytic unfoldings of some Hopf-Zero singularities through a beyond all order phenomenon: the exponentially small breakdown of invariant ...
  • Dynamics in a time-discrete food-chain model with strong pressure on preys 

    Lázaro Ochoa, José Tomás; Alsedà, Lluís; Vidiella, Blai; Solé Vicente, Ricard; Sardañés, Josep (2020-05-01)
    Article
    Restricted access - publisher's policy
    Discrete-time dynamics, mainly arising in boreal and temperate ecosystems for species with non-overlapping generations, have been largely studied to understand the dynamical outcomes due to changes in relevant ecological ...
  • A geometric approach to phase response curves and its numerical computation through the parameterization method 

    Pérez Cervera, Alberto; Martínez-Seara Alonso, M. Teresa; Huguet Casades, Gemma (2019-01-01)
    Article
    Open Access
    The phase response curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper, we present a new ...
  • Dinàmica de varietats espacials: les autopistes de l’univers 

    Ollé Torner, Mercè; Barrabés Vera, Esther (2019-12-20)
    Article
    Open Access
    En aquest article volem il.lustrar com la comprensió de la dinàmica d’alguns models de la mecànica celeste permet explicar alguns fenòmens astronòmics i dissenyar missions realistes a l’espai. El model paradigmàtic usat ...
  • Phase-amplitude dynamics in terms of extended response functions: invariant curves and arnold tongues 

    Guillamon Grabolosa, Antoni; Castejón Company, Oriol (2019)
    Article
    Open Access
    Phase response curves (PRCs) have been extensively used to control the phase of oscillators under perturbations. Their main advantage is the reduction of the whole model dynamics to a single variable (phase) dynamics. ...
  • Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies 

    Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (2019-06)
    External research report
    Open Access
    We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional ...
  • Asymptotic density of collision orbits in the restricted circular planar 3 body problem 

    Guàrdia Munarriz, Marcel; Kaloshin, Vadim; Zhang, Jianlu (2019-03-12)
    Article
    Open Access
    For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(µ120) dense as µ¿0 .
  • Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (II): The generic case 

    Baldomá Barraca, Inmaculada; Castejón Company, Oriol; Martínez-Seara Alonso, M. Teresa (2018-04-17)
    Article
    Open Access
    In this paper, we prove the breakdown of the two-dimensional stable and unstable manifolds associated to two saddle-focus points which appear in the unfoldings of the Hopf-zero singularity. The method consists in obtaining ...
  • Nonlinear estimation of synaptic conductances via piecewise linear systems 

    Guillamon Grabolosa, Antoni; Prohens Sastre, Rafel; Teruel Aguilar, Antonio E.; Vich Llompart, Catalina (Birkhäuser Basel, 2017)
    Conference lecture
    Open Access
    This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the
  • Dynamics around the triangular libration points of 1999 KW4 

    Yuying, Liang; Gómez Muntané, Gerard; Masdemont Soler, Josep; Ming, Xu (2018)
    Conference report
    Restricted access - publisher's policy
    His paper studies the dynamics of stable regions for relatively long time intervals (practical stability) in the vicinity of the triangular equilibrium points of a binary asteroid with mass ratio µ larger than Rouths ...

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