Browsing by Author "Martínez-Seara Alonso, M. Teresa"
Now showing items 21-40 of 71
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Critical velocity in kink-defect interaction models: rigorous results
(2020-01-01)
Article
Open AccessIn this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More ... -
Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
(2011-07)
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 Hopf-Zero Singularity
(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 Hopf-zero 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
(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: Flow-box coordinates and upper bounds
(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 nearly-integrable Hamiltonian near a simple resonance. The model consists of an integrable Hamiltonian ... -
Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results
(2011)
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 non-autonomous perturbation which is fast and periodic in time. We provide ... -
Exponentially small splitting of separatrices in the perturbed McMillan map
(2009-12)
Research report
Open AccessThe McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. ... -
Exponentially small splitting of separatrices in the perturbed McMillan map
(2011-10)
Article
Open AccessThe McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic xed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. ... -
Exponentially small splitting of separatrices under fast quasiperiodic forcing
(1997)
Article
Open AccessWe consider fast quasiperiodic perturbations with two frequencies $(1/\varepsilon,\gamma/\varepsilon)$ of a pendulum, where $\gamma$ is the golden mean number. The complete system has a two-dimensional invariant ... -
Generalized analytical results on n-ejection–collision orbits in the RTBP: analysis of bifurcations
(Springer Nature, 2023-02-01)
Article
Open AccessIn the planar circular restricted three-body problem and for any value of the mass parameter µ¿(0,1) and n=1 , we prove the existence of four families of n-ejection–collision (n-EC) orbits, that is, orbits where the particle ... -
Generic bifurcations of low codimension of planar Filippov Systems
(2011-02)
Article
Restricted access - publisher's policyIn this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local(and global) bifurcations in ... -
Generic bifurcations of low codimension of planar Filippov Systems
(2009-10)
Research report
Open AccessIn this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local (and global) bifurcations ... -
Global phase-amplitude description of oscillatory dynamics via the parameterization method
(Institute of Physics (IOP), 2020-08-01)
Article
Open AccessIn this paper, we use the parameterization method to provide a complete description of the dynamics of an n-dimensional oscillator beyond the classical phase reduction. The parameterization method allows us, via efficient ... -
Hopf-Zero singularities truly unfold chaos
(2020-05-01)
Article
Open AccessWe 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 ... -
Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion
(2013-06)
Research report
Open AccessAbstract. We consider models given by Hamiltonians of the form H ( I;';p;q;t ; " ) = h ( I )+ n X j =1 1 2 p 2 j + V j ( q j ) + "Q ( I;';p;q;t ; " ) where I 2I R d ;' 2 T d ... -
Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion
(2016-05-14)
Article
Open AccessWe consider models given by Hamiltonians of the form View the MathML sourceH(I,f,p,q,t;e)=h(I)+¿j=1n±(12pj2+Vj(qj))+eQ(I,f,p,q,t;e) Turn MathJax on where I¿I¿Rd,f¿TdI¿I¿Rd,f¿Td, p,q¿Rnp,q¿Rn, t¿T1t¿T1. These are higher ... -
Kolmogórov: la K del teorema KAM. Lliçó inaugural Curs Kolmogórov (2021-2022)
(2021-11-25)
Audiovisual
Open AccessLliçó inaugural del curs 2021-2022 a càrrec de la professora Tere Martínez-Seara amb el títol "Kolmogórov: la K del teorema KAM". El curs 2021-2022 de l'FME està dedicat a Andrei N. Kolmogórov -
Les varietats invariants i el seu paper en els sistemes dinàmics: de les òrbites dels cometes a les ones cerebrals
(2022-05-11)
Audiovisual
Open AccessCicle de Xerrades Panoràmiques sobre temes de recerca d'actualitat adreçades a estudiants i joves investigadors -
Local generic behavior of a planar Filippov system with non-smooth switching curve
(Springer Nature, 2021-10-18)
Article
Open AccessThis paper discusses the generic local classification of typical singularities of 2D piecewise smooth vector fields when the switching set is an non smooth curve. The main goal is to obtain classification results concerning ... -
Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing
(1997)
Article
Open AccessQuasiperiodic perturbations with two frequencies $(1/\varepsilon ,\gamma /\varepsilon )$ of a pendulum are considered, where $\gamma $ is the golden mean number. We study the splitting of the three-dimensional invariant ...
