# Person: 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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0000-0002-0974-6656

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1715

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Publication Open Access Singular reduction of resonant Hamiltonians(IOP Publishing, 2018) Meyer, Kenneth Ray; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e InformáticaShow more We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built using normal forms and applying reduction theory obtaining the reduced Hamiltonian that is defined on the orbit space. Generically, the reduction is of singular character and we classify the singularities in the orbit space, getting three different types of singular points. A critical point of the reduced Hamiltonian corresponds to a family of periodic solutions in the full system whose characteristic multipliers are approximated accordingly to the nature of the critical point.Show more Publication Open Access Nonlinear stability of elliptic equilibria in Hamiltonian systems with exponential time estimates(American Institute of Mathematical Sciences (AIMS), 2021) Cárcamo Díaz, Daniela Jacqueline; Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasShow more In the framework of nonlinear stability of elliptic equilibria in Hamiltonian systems with n degrees of freedom we provide a criterion to obtain a type of formal stability, called Lie stability. Our result generalises previous approaches, as exponential stability in the sense of Nekhoroshev (excepting a few situations) and other classical results on formal stability of equilibria. In case of Lie stable systems we bound the solutions near the equilibrium over exponentially long times. Some examples are provided to illustrate our main contributions.Show more Publication Open Access On the nonlinear stability of the triangular points in the circular spatial restricted three-body problem(Pleiades Publishing, 2020) Cárcamo Díaz, Daniela Jacqueline; Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasShow more The well-known problem of the nonlinear stability of L4 and L5 in the circular spatial restricted three-body problem is revisited. Some new results in the light of the concept of Lie (formal) stability are presented. In particular, we provide stability and asymptotic estimates for three specific values of the mass ratio that remained uncovered. Moreover, in many cases we improve the estimates found in the literature.Show more Publication Open Access On co-orbital quasi-periodic motion in the three-body problem(Society for Industrial and Applied Mathematics (SIAM), 2019) Cors, Josep Maria; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasShow more Within the framework of the planar three-body problem we establish the existence of quasi-periodic motions and KAM 4-tori related to the co-orbital motion of two small moons about a large planet where the moons move in nearly circular orbits with almost equal radii. The approach is based on a combination of normal form and symplectic reduction theories and the application of a KAM theorem for high-order degenerate systems. To accomplish our results we need to expand the Hamiltonian of the three-body problem as a perturbation of two uncoupled Kepler problems. This approximation is valid in the region of phase space where co-orbital solutions occur.Show more 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 MatemáticasShow more In 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.Show more Publication Open Access Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance(Springer, 2018) Carrasco, Dante; Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Vidarte, Jhon; Yanguas Sayas, Patricia; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e InformáticaShow more We study the dynamics of a family of perturbed three-degree-of-freedom Hamiltonian systems which are in 1:1:1 resonance. The perturbation consists of axially symmetric cubic and quartic arbitrary polynomials. Our analysis is performed by normalisation, reduction and KAM techniques. Firstly, the system is reduced by the axial symmetry, and then, periodic solutions and KAM 3-tori of the full system are determined from the relative equilibria. Next, the oscillator symmetry is extended by normalisation up to terms of degree 4 in rectangular coordinates; after truncation of higher orders and reduction to the orbit space, some relative equilibria are established and periodic solutions and KAM 3-tori of the original system are obtained. As a third step, the reduction in the two symmetries leads to a one-degree-of-freedom system that is completely analysed in the twice reduced space. All the relative equilibria together with the stability and parametric bifurcations are determined. Moreover, the invariant 2-tori (related to the critical points of the twice reduced space), some periodic solutions and the KAM3-tori, all corresponding to the full system, are established. Additionally, the bifurcations of equilibria occurring in the twice reduced space are reconstructed as quasi-periodic bifurcations involving 2-tori and periodic solutions of the full system.Show more Publication Open Access Bright fireballs recorded along February 2021 in the framework of the Southwestern Europe Meteor Network(MeteorNews, 2021) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasShow more This work focuses on the analysis of some of the brightest bolides recorded along February 2021 by the meteorobserving stations operating in the framework of the Southwestern Europe Meteor Network (SWEMN). Some of them were produced by meteoroids belonging to recently discovered and poorly-known streams. The absolute magnitude of these fireballs, which were observed over the Iberian Peninsula, ranged between ±7 and ±10. The emission spectra produced by some of these events are also presented and discussed.Show more Publication Open Access Bright fireballs recorded along March 2021 in the framework of the Southwestern Europe Meteor Network(MeteorNews, 2021) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasShow more We present here some recent improvements performed in the framework of the Southwestern Europe Meteor Network (SWEMN) and the SMART project. In particular, we focus on the development of the first digital database dedicated to meteor events recorded over Spain and neighboring areas. This includes, among other information, the circumstances of each event, orbital data, emission spectrum, lightcurve, and meteoroid physical properties. We also discuss in this work the main fireballs recorded by our network along April 2021.Show more Publication Open Access Corrigendum to “Oscillatory motions in restricted N-body problems” [J. Differential Equations 265 (2018) 779–803](Elsevier, 2019) Álvarez-Ramírez, Martha; Rodríguez García, Antonio; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasShow more At the beginning of paper [1] there is an error that spreads along the rest of the work and the conclusions are not correct in their present form. Precisely, in Section 2, page 783, there is a contradiction related to the scaling. In the paragraph before formula (6) it is said that t→ε^3t but Hamiltonian (6) is not scaled accordingly. We have fixed the problem and, after performing due changes, the conclusions are obtained. The existence of the manifolds at infinity is guaranteed (Theorem 3.1) and the transversal intersection of them is concluded in Theorem 5.1. The applications in Section 6 are also valid after adapting them to the new version of the theorems.Show more Publication Open Access Hill problem analytical theory to the order four: application to the computation of frozen orbits around planetary satellites(Hindawi Publishing Corporation, 2009) Lara, Martín; Palacián Subiela, Jesús Francisco; Ingeniería Matemática e Informática; Matematika eta Informatika IngeniaritzaShow more Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that connects the averaged and nonaveraged models. A fourth-order analytical theory is necessary for the accurate computation of quasi-periodic frozen orbits.Show more