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 Matemáticas
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.
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 Matemáticas
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.
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 Matemáticas
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.
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
FRIPON: a worldwide network to track incoming meteoroids
(EDP Sciences, 2020) Colas, F.; Zanda, B.; Bouley, S.; Jeanne, S.; Malgoyre, A.; Birlan, M.; Yanguas Sayas, Patricia; Blanpain, C.; Gattacceca, J.; Jorda, L.; Lecubin, J.; Marmo, C.; Rault, J. L.; Vaubaillon, J.; Vernazza, P.; Yohia, C.; Gardiol, D.; Nedelcu, A.; Poppe, B.; Rowe, J.; Forcier, M.; Koschny, D.; Trigo-Rodríguez, J. M.; Lamy, H.; Behrend, R.; Ferrière, L.; Barghini, D.; Buzzoni, A.; Carbognani, A.; Di Carlo, M.; Di Martino, M.; Knapic, C.; Londero, E.; Pratesi, G.; Rasetti, S.; Riva, W.; Stirpe, G.M.; Valsecchi, G.B.; Volpicelli, C.A.; Zorba, S.; Coward, D.; Drolshagen, E.; Drolshagen, G.; Hernández, O.; Jehin, E.; Jobin, M.; King, A.; Nitschelm, C.; Ott, T.; Sánchez-Lavega, Agustín; Toni, A.; Abraham, P.; Affaticati, F.; Albani, M.; Andreis, A.; Andrieu, T.; Anghel, S.; Antaluca, E.; Antier, K.; Appéré, T.; Armand, A.; Ascione, G.; Audureau, Y.; Auxepaules, G.; Avoscan, T.; Baba Aissa, D.; Bacci, P.; Bãdescu, O.; Baldini, R.; Baldo, R.; Balestrero, A.; Baratoux, D.; Barbotin, E.; Bardy, M.; Basso, S.; Bautista, O.; Bayle, L. D.; Beck, P.; Bellitto, R.; Belluso, R.; Benna, C.; Benammi, M.; Beneteau, E.; Benkhaldoun, Z.; Bergamini, P.; Bernardi, F.; Bertaina, M. E.; Bessin, P.; Betti, L.; Bettonvil, F.; Bihel, D.; Birnbaum, C.; Blagoi, O.; Blouri, E.; Boacã, I.; Boatã, R.; Bobiet, B.; Bonino, R.; Boros, K.; Bouchet, E.; Borgeot, V.; Bouchez, E.; Boust, D.; Boudon, V.; Bouman, T.; Bourget, P.; Brandenburg, S.; Bramond, Ph.; Braun, E.; Bussi, A.; Cacault, P.; Caillier, B.; Calegaro, A.; Camargo, J.; Caminade, S.; Campana, A. P. C.; Campbell Burns, P.; Canal Domingo, R.; Carell, O.; Carreau, S.; Cascone, E.; Cattaneo, C.; Cauhape, P.; Cavier, P.; Celestin, S.; Cellino, A.; Champenois, M.; Chennaoui Aoudjehane, Hasnaa; Chevrier, S.; Cholvy, P.; Chomier, L.; Christou, A.; Cricchio, D.; Coadou, P.; Cocaign, J. Y.; Cochard, F.; Cointin, S.; Colombi, E.; Colque Saavedra, J. P.; Corp, L.; Costa, M.; Costard, F.; Cottier, M.; Cournoyer, P.; Cousta, E.; Cremonese, G.; Cristea, O.; Cuzon, J. C.; D’Agostino, G.; Daiffallah, K.; Dãnescu, C.; Dardon, A.; Dasse, T.; Davadan, C.; Debs, V.; Defaix, J. P.; Deleflie, F.; D’Elia, M.; Luca, P. de; Maria, P. de; Deverchère, P.; Devillepoix, H.; Dias, A.; Di Dato, Andrea; Di Luca, R.; Dominici, F. M.; Drouard, A.; Dumont, J. L.; Dupouy, P.; Duvignac, L.; Egal, A.; Erasmus, N.; Esseiva, N.; Ebel, A.; Eisengarten, B.; Federici, F.; Feral, S.; Ferrant, G.; Ferreo, E.; Finitzer, P.; Foucault, A.; Francois, P.; Frîncu, M.; Froger, J. L.; Gaborit, F.; Gagliarducci, V.; Galard, J.; Gardavot, A.; Garmier, M.; Garnung, M.; Gautier, B.; Gendre, B.; Gerard, D.; Gerardi, A.; Godet, J. P.; Grandchamps, A.; Grouiez, B.; Groult, S.; Guidetti, D.; Giuli, G.; Hello, Y.; Henry, X.; Herbreteau, G.; Herpin, M.; Hewins, P.; Hillairet, J. J.; Horak, J.; Hueso, R.; Huet, E.; Huet, S.; Hyaumé, F.; Interrante, G.; Isselin, Y.; Jeangeorges, Y.; Janeux, P.; Jeanneret, P.; Jobse, K.; Jouin, S.; Jouvard, J. M.; Joy, K.; Julien, F.; Kacerek, R.; Kaire, M.; Kempf, M.; Krier, C.; Kwon, M. K.; Lacassagne, L.; Lachat, D.; Lagain, A.; Laisné, E.; Lanchares, Víctor; Laskar, J.; Lazzarin, M.; Leblanc, M.; Lebreton, J. P.; Lecomte, J.; Le Dû, P.; Lelong, F.; Lera, S.; Leoni, J. F.; Le Pichon, A.; Le Poupon, P.; Leroy, A.; Leto, G.; Levansuu, A.; Lewin, E.; Lienard, A.; Licchelli, D.; Locatelli, H.; Loehle, S.; Loizeau, D.; Luciani, L.; Maignan, M.; Manca, F.; Mancuso, S.; Mandon, E.; Mangold, N.; Mannucci, F.; Maquet, L.; Marant, D.; Marchal, Y.; Marín, J. L.; Martín Brisset, J. C.; Martín, D.; Mathieu, D.; Maury, A.; Mespoulet, N.; Meyer, F.; Meyer, J. Y.; Meza, E.; Moggi Cecchi, V.; Moiroud, J. J.; Millán, M.; Montesarchio, M.; Misiano, A.; Molinari, E.; Molau, S.; Monari, J.; Monflier, B.; Monkos, A.; Montemaggi, M.; Monti, G.; Moreau, R.; Morin, J.; Mourgues, R.; Mousis, O.; Nablanc, C.; Nastasi, A.; Niacsu, L.; Notez, P.; Ory, M.; Pace, E.; Paganelli, M. A.; Pagola, A.; Pajuelo, M.; Palacián Subiela, Jesús Francisco; Pallier, G.; Paraschiv, P.; Pardini, R.; Pavone, M.; Pavy, G.; Payen, G.; Pegoraro, A.; Peña-Asensio, Eloy; Pérez, L.; Pérez-Hoyos, Santiago; Perlerin, V.; Peyrot, A.; Peth, F.; Pic, V.; Pietronave, S.; Pilger, C.; Piquel, M.; Pisanu, T.; Poppe, M.; Portois, L.; Prezeau, J. F.; Pugno, N.; Quantin, C.; Quitté, G.; Rambaux, N.; Ravier, E.; Repetti, U.; Ribas, S.; Richard, C.; Richard, D.; Rigoni, M.; Rivet, J. P.; Rizzi, N.; Rochain, S.; Rojas, J. F.; Romeo, M.; Rotaru, M.; Rotger, M.; Rougier, P.; Rousselot, P.; Rousset, J.; Rousseu, D.; Rubiera, O.; Rudawska, R.; Rudelle, J.; Ruguet, J. P.; Russo, P.; Sales, S.; Sauzereau, O.; Salvati, F.; Schieffer, M.; Schreiner, D.; Scribano, Y.; Selvestrel, D.; Serra, R.; Shengold, L.; Shuttleworth, A.; Smareglia, R.; Sohy, S.; Soldi, M.; Stanga, R.; Steinhausser, A.; Strafella, F.; Sylla, Serigne; Smedley, Andrew; Tagger, M.; Tanga, P.; Taricco, C.; Teng, J. P.; Tercu, J. O.; Thizy, O.; Thomas, J. P.; Tombelli, M.; Trangosi, R.; Tregon, B.; Trivero, P.; Tukkers, A.; Turcu, V.; Umbriaco, G.; Unda-Sanzana, Eduardo; Vairetti, R.; Valenzuela, M.; Valente, G.; Varennes, G.; Vauclair, S.; Vergne, J.; Verlinden, M.; Vidal Alaiz, M.; Vieira-Martins, Roberto; Viel, A.; Vîntdevarã, D. C.; Vinogradoff, V.; Volpini, P.; Wendling, M.; Wilhelm, P.; Wohlgemuth, K.; Zagarella, R.; Zollo, A.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
Context. Until recently, camera networks designed for monitoring fireballs worldwide were not fully automated, implying that in case of a meteorite fall, the recovery campaign was rarely immediate. This was an important limiting factor as the most fragile - hence precious - meteorites must be recovered rapidly to avoid their alteration. Aims. The Fireball Recovery and InterPlanetary Observation Network (FRIPON) scientific project was designed to overcome this limitation. This network comprises a fully automated camera and radio network deployed over a significant fraction of western Europe and a small fraction of Canada. As of today, it consists of 150 cameras and 25 European radio receivers and covers an area of about 1.5 × 106km2. Methods. The FRIPON network, fully operational since 2018, has been monitoring meteoroid entries since 2016, thereby allowing the characterization of their dynamical and physical properties. In addition, the level of automation of the network makes it possible to trigger a meteorite recovery campaign only a few hours after it reaches the surface of the Earth. Recovery campaigns are only organized for meteorites with final masses estimated of at least 500 g, which is about one event per year in France. No recovery campaign is organized in the case of smaller final masses on the order of 50 to 100 g, which happens about three times a year; instead, the information is delivered to the local media so that it can reach the inhabitants living in the vicinity of the fall. Results. Nearly 4000 meteoroids have been detected so far and characterized by FRIPON. The distribution of their orbits appears to be bimodal, with a cometary population and a main belt population. Sporadic meteors amount to about 55% of all meteors. A first estimate of the absolute meteoroid flux (mag < -5; meteoroid size ≥∼1 cm) amounts to 1250/yr/106km2. This value is compatible with previous estimates. Finally, the first meteorite was recovered in Italy (Cavezzo, January 2020) thanks to the PRISMA network, a component of the FRIPON science project. © The Author(s), 2020.
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: 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
Remarkable fireballs spotted in the framework of the Southwestern Europe Meteor Network along August and September 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, Antonio; Aimee, A. I.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
Some of the bright bolides observed in the framework of the Southwestern Europe Meteor Network between August and September 2022 are described in this work. These have been spotted from the Iberian Peninsula. Their maximum luminosity ranges from mag. –7 to mag. –12. One of these bolides gave rise to a meteorite.
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.