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 Informática
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.
Open Access
The Southwestern Europe Meteor Network: remarkable bolides recorded from March to May 2022
(MeteorNews, 2022) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; San Segundo, A.; Ávila, D.; Tosar, Borja; Gómez-Hernández, A.; Gómez-Martínez, Juan; García, A.; Aimee, A. I.; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Some of the remarkable bolides spotted in the framework of the Southwestern Europe Meteor Network from March to May 2022 are described here. These have been observed from the Iberian Peninsula. Their absolute magnitude ranges from -8 to -15. The emission spectrum of one of them is also analyzed. Bright meteors included in this report were linked to different sources: the sporadic background, major meteoroid streams, and poorly-known streams.
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 Matemáticas
We 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.
Open Access
The Southwestern Europe Meteor Network: new advances and analysis of bright fireballs recorded from September to December 2021
(MeteorNews, 2022) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; San Segundo, A.; Ávila, D.; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
In this work we focus on some recent improvements performed in the framework of the Southwestern Europe Meteor Network (SWEMN) and the SMART project. Thus, by employing artificial intelligence methods, we have significantly enhanced the capabilities of our fireball database to automatically disseminate its most remarkable contents through social networks and other channels. This is the first digital database dedicated to meteor events recorded over Spain and neighboring areas. In addition, we have expanded our network by deploying new meteor cameras. We also present in this work the most relevant fireballs recorded by SWEMN from September to December 2021, including the emission spectrum of some of these events.
Open Access
Oscillatory motions in restricted N-body problems
(Elsevier, 2018) Álvarez-Ramírez, Martha; Rodríguez García, Antonio; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática
We consider the planar restricted N-body problem where the N−1 primaries are assumed to be in a central configuration whereas the infinitesimal particle escapes to infinity in a parabolic orbit. We prove the existence of transversal intersections between the stable and unstable manifolds of the parabolic orbits at infinity which guarantee the existence of a Smale’s horseshoe. This implies the occurrence of chaotic mo-tions, namely the oscillatory motions, that is, orbits for which the massless particle leaves every bounded region but it returns infinitely often to some fixed bounded region. Our achievement is based in an adequate scaling of the variables which allows us to write the Hamiltonian function as the Hamiltonian of the Kepler problem plus higher-order terms that depend on the chosen configuration. We compute the Melnikov function related to the first non-null perturbative term and characterize the cases where it has simple zeroes. Concretely, for some combinations of the configuration parameters, i.e. mass values and positions of the primaries, and for a specific value of a parameter related to the angular momentum vector, the Melnikov function vanishes, otherwise it has simple zeroes and the transversality condition is satisfied. When the Melnikov function corresponding to the principal part of the perturbation is zero we compute the next non-zero Melnikov function proving that it has simple zeroes. The theory is illustrated for various cases of restricted N-body problems, including the circular restricted three-body problem. No restrictions on the mass parameters are assumed.
Open Access
The Southwestern Europe Meteor Network: recent advances and analysis of bright fireballs recorded along April 2021
(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; San Segundo, A.; Ávila, D.; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
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.
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 Ingeniaritza
We 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.
Open Access
Dynamics in the charged restricted circular three-body problem
(Springer US, 2018) Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Vidarte, Jhon; Yanguas Sayas, Patricia; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The existence and stability of periodic solutions for different types of perturbations associated to the Charged Restricted Circular Three Body Problem (shortly, CHRCTBP) is tackled using reduction and averaging theories as well as the technique of continuation of Poincaré for the study of symmetric periodic solutions. The determination of KAM 2-tori encasing some of the linearly stable periodic solutions is proved. Finally, we analyze the occurrence of Hamiltonian-Hopf bifurcations associated to some equilibrium points of the CHRCTBP.
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 Matemáticas
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.
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 Matemáticas
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.