Palacián Subiela, Jesús Francisco
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Palacián Subiela
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Jesús Francisco
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Estadística, Informática y Matemáticas
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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas
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Publication Open Access Reeb’s theorem and periodic orbits for a rotating Hénon–Heiles potential(Springer, 2019) Lanchares, Víctor; Pascual, Ana Isabel; Iñarrea, Manuel; Salas, José Pablo; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasWe apply Reeb’s theorem to prove the existence of periodic orbits in the rotating Hénon– Heiles system. To this end, a sort of detuned normal form is calculated that yields a reduced system with at most four non degenerate equilibrium points. Linear stability and bifurcations of equilibrium solutions mimic those for periodic solutions of the original system. We also determine heteroclinic connections that can account for transport phenomena.Publication Open Access Magnetic confinement of a neutral atom in a double-wire waveguide: a nonlinear dynamics approach(Elsevier, 2021) Salas, José Pablo; Iñarrea, Manuel; Lanchares, Víctor; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Estadística, Informática y MatemáticasIn this paper we focus on the classical dynamics of a neutral atom trapped in a doublewire waveguide in the presence of two uniform bias fields. Because the trapping region takes place in a plane perpendicular to the (parallel) wires, the dynamics is governed by a two-degrees of freedom Hamiltonian where, besides the energy, the two bias fields are the relevant system’s parameters. An exhaustive study of the critical points of the potential energy surface, their stability and bifurcations is carried out, so that, two different trapping regions are characterized. The dynamics in each of these regions is studied by applying classical perturbation theory, which provides an integrable approximation of the original Hamiltonian. The dynamics arising from this normalized Hamiltonian (stability of the equilibrium points, their bifurcations and the phase flow evolution) is then analyzed in a convenient set of phase variables. Poincaré surfaces of section to describe the structure and evolution of the phase space governed by the full Hamiltonian are also used. A complete agreement between the descriptions of the dynamics provided by the perturbation theory and the numerical studies is obtained.Publication Open Access Charge transfer in the Rydberg hydrogen atom metal surface interaction: a transition state approach(2007) Salas, José Pablo; Iñarrea, Manuel; Lanchares, Víctor; Palacián Subiela, Jesús Francisco; Pascual, Ana Isabel; Yanguas Sayas, Patricia; Ingeniería Matemática e Informática; Matematika eta Informatika IngeniaritzaWe study the classical dynamics of a hydrogen atom near a metallic surface in the presence of a uniform electric field. By continuation of families of periodic orbits and surfaces of section we show that, due to the electric field, the atom falls into a Stark regime through two pitchfork bifurcations. The charge transfer is studied by using the Dynamical Transition State Theory. Indeed, we obtain analytically the geometrical structures that in phase space regulate the ionisation of the atom and we calculate efficiently the ionisation probability as a function of the electric field strength.