Reports de recerca
http://hdl.handle.net/2117/3919
2018-02-18T10:57:16ZReport on the EGNSS competition after Y2
http://hdl.handle.net/2117/114076
Report on the EGNSS competition after Y2
Sanz Subirana, Jaume; Juan Zornoza, José Miguel; Alonso Alonso, María Teresa; Povero, Gabriella
2018-02-13T12:40:33ZSanz Subirana, JaumeJuan Zornoza, José MiguelAlonso Alonso, María TeresaPovero, GabriellaThe geometry of E-manifolds
http://hdl.handle.net/2117/114021
The geometry of E-manifolds
Miranda Galcerán, Eva
Motivated by the study of symplectic Lie algebroids, we
study a describe a type of algebroid (called an E-tangent bundle) which
is particularly well-suited to study of singular differential forms and
their cohomology. This setting generalizes the study of b-symplectic
manifolds, foliated manifolds, and a wide class of Poisson manifolds.
We generalize Moser's theorem to this setting, and use it to construct
symplectomorphisms between singular symplectic forms. We give appli-
cations of this machinery (including the study of Poisson cohomology),
and study specific examples of a few of them in depth.
2018-02-12T09:13:57ZMiranda Galcerán, EvaMotivated by the study of symplectic Lie algebroids, we
study a describe a type of algebroid (called an E-tangent bundle) which
is particularly well-suited to study of singular differential forms and
their cohomology. This setting generalizes the study of b-symplectic
manifolds, foliated manifolds, and a wide class of Poisson manifolds.
We generalize Moser's theorem to this setting, and use it to construct
symplectomorphisms between singular symplectic forms. We give appli-
cations of this machinery (including the study of Poisson cohomology),
and study specific examples of a few of them in depth.Periodic points of a Landen transformation
http://hdl.handle.net/2117/112835
Periodic points of a Landen transformation
Gasull Embid, Armengol; Llorens, Mireia; Mañosa Fernández, Víctor
We prove the existence of 3-periodic orbits in a dynamical system associated to a Landen transformation previously studied by Boros, Chamberland and Moll, disproving a conjecture on the dynamics of this planar map introduced by the latter author. To this end we present a systematic methodology to determine and locate analytically isolated periodic points of algebraic maps. This approach can be useful to study other discrete dynamical systems with algebraic nature. Complementary results on the dynamics of the map associated with the Landen transformation are also presented.
Preprint
2018-01-16T12:20:20ZGasull Embid, ArmengolLlorens, MireiaMañosa Fernández, VíctorWe prove the existence of 3-periodic orbits in a dynamical system associated to a Landen transformation previously studied by Boros, Chamberland and Moll, disproving a conjecture on the dynamics of this planar map introduced by the latter author. To this end we present a systematic methodology to determine and locate analytically isolated periodic points of algebraic maps. This approach can be useful to study other discrete dynamical systems with algebraic nature. Complementary results on the dynamics of the map associated with the Landen transformation are also presented.Some manifolds of periodic orbits in the restricted three body problem
http://hdl.handle.net/2117/111091
Some manifolds of periodic orbits in the restricted three body problem
Gómez Muntané, Gerard; Noguera Batlle, Miquel
In the present paper we give some numerical results about natural families of periodic orbits, which emanate from limiting orbits around equilateral equilibrium points of the Restricted Three Body Problem, when the mass ratio is grater than Routh's critical one.; En aquest article es presenten els resultats numèrics obtinguts sobre les famílies naturals d'òrbites periòdiques al voltant del punt L4 del problema restringit circular i la de tres cossos, per a valors del paràmetre de massa superiors a la massa crítica de Routh
2017-11-22T18:08:56ZGómez Muntané, GerardNoguera Batlle, MiquelIn the present paper we give some numerical results about natural families of periodic orbits, which emanate from limiting orbits around equilateral equilibrium points of the Restricted Three Body Problem, when the mass ratio is grater than Routh's critical one.
En aquest article es presenten els resultats numèrics obtinguts sobre les famílies naturals d'òrbites periòdiques al voltant del punt L4 del problema restringit circular i la de tres cossos, per a valors del paràmetre de massa superiors a la massa crítica de RouthLocating domination in bipartite graphs and their complements
http://hdl.handle.net/2117/111067
Locating domination in bipartite graphs and their complements
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
A set S of vertices of a graph G is distinguishing if the sets of neighbors in S for every pair of vertices not in S are distinct. A locating-dominating set of G is a dominating distinguishing set. The location-domination number of G , ¿ ( G ), is the minimum cardinality of a locating-dominating set. In this work we study relationships between ¿ ( G ) and ¿ ( G ) for bipartite graphs. The main result is the characterization of all connected bipartite graphs G satisfying ¿ ( G ) = ¿ ( G ) + 1. To this aim, we define an edge-labeled graph G S associated with a distinguishing set S that turns out to be very helpful
2017-11-22T12:08:39ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelA set S of vertices of a graph G is distinguishing if the sets of neighbors in S for every pair of vertices not in S are distinct. A locating-dominating set of G is a dominating distinguishing set. The location-domination number of G , ¿ ( G ), is the minimum cardinality of a locating-dominating set. In this work we study relationships between ¿ ( G ) and ¿ ( G ) for bipartite graphs. The main result is the characterization of all connected bipartite graphs G satisfying ¿ ( G ) = ¿ ( G ) + 1. To this aim, we define an edge-labeled graph G S associated with a distinguishing set S that turns out to be very helpfulMetric-locating-dominating partitions in graphs
http://hdl.handle.net/2117/111061
Metric-locating-dominating partitions in graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
A partition ¿ = { S 1 ,...,S k } of the vertex set of a connected graph G is a metric-locating partition of G if for every pair of vertices u,v belonging to the same part S i , d ( u,S j ) 6 = d ( v,S j ), for some other part S j . The partition dimension ß p ( G ) is the minimum cardinality of a metric- locating partition of G . A metric-locating partition ¿ is called metric-locating-dominanting if for every vertex v of G , d ( v,S j ) = 1, for some part S j of ¿. The partition metric-location-domination number ¿ p ( G ) is the minimum cardinality of a metric-locating-dominating partition of G . In this paper we show, among other results, that ß p ( G ) = ¿ p ( G ) = ß p ( G ) + 1. We also charac- terize all connected graphs of order n = 7 satisfying any of the following conditions: ¿ p ( G ) = n - 1, ¿ p ( G ) = n - 2 and ß p ( G ) = n - 2. Finally, we present some tight Nordhaus-Gaddum bounds for both the partition dimension ß ( G ) and the partition metric-location-domination number ¿ ( G ). Keywords: dominating partition, locating partition, location, domination, metric location
2017-11-22T11:22:19ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelA partition ¿ = { S 1 ,...,S k } of the vertex set of a connected graph G is a metric-locating partition of G if for every pair of vertices u,v belonging to the same part S i , d ( u,S j ) 6 = d ( v,S j ), for some other part S j . The partition dimension ß p ( G ) is the minimum cardinality of a metric- locating partition of G . A metric-locating partition ¿ is called metric-locating-dominanting if for every vertex v of G , d ( v,S j ) = 1, for some part S j of ¿. The partition metric-location-domination number ¿ p ( G ) is the minimum cardinality of a metric-locating-dominating partition of G . In this paper we show, among other results, that ß p ( G ) = ¿ p ( G ) = ß p ( G ) + 1. We also charac- terize all connected graphs of order n = 7 satisfying any of the following conditions: ¿ p ( G ) = n - 1, ¿ p ( G ) = n - 2 and ß p ( G ) = n - 2. Finally, we present some tight Nordhaus-Gaddum bounds for both the partition dimension ß ( G ) and the partition metric-location-domination number ¿ ( G ). Keywords: dominating partition, locating partition, location, domination, metric locationDominating 2- broadcast in graphs: complexity, bounds and extremal graphs
http://hdl.handle.net/2117/109101
Dominating 2- broadcast in graphs: complexity, bounds and extremal graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Cáceres, José; Puertas, M. Luz
Limited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded. As a natural extension of domination, we consider dominating 2-broadcasts along with the associated parameter, the dominating 2-broadcast number. We prove that computing the dominating 2-broadcast number is a NP-complete problem, but can be achieved in linear time for trees. We also give an upper bound for this parameter, that is tight for graphs as large as desired
2017-10-25T05:28:42ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelCáceres, JoséPuertas, M. LuzLimited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded. As a natural extension of domination, we consider dominating 2-broadcasts along with the associated parameter, the dominating 2-broadcast number. We prove that computing the dominating 2-broadcast number is a NP-complete problem, but can be achieved in linear time for trees. We also give an upper bound for this parameter, that is tight for graphs as large as desiredBifurcation of 2-periodic orbits from non-hyperbolic fixed points
http://hdl.handle.net/2117/106815
Bifurcation of 2-periodic orbits from non-hyperbolic fixed points
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2-periodic orbits that can bifurcate from the fixed point. As an application we study the 2-cyclicity of some natural families of polynomial maps.
Prepublicació
2017-07-25T11:28:59ZCima Mollet, AnnaGasull Embid, ArmengolMañosa Fernández, VíctorWe introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2-periodic orbits that can bifurcate from the fixed point. As an application we study the 2-cyclicity of some natural families of polynomial maps.Geometric quantization of semitoric systems and almost toric manifolds
http://hdl.handle.net/2117/106532
Geometric quantization of semitoric systems and almost toric manifolds
Miranda Galcerán, Eva; Presas, Francisco; Solha, Romero
Kostant gave a model for the real geometric quantization
associated to polarizations via the cohomology associated to the sheaf of
flat sections of a pre-quantum line bundle. This model is well-adapted
for real polarizations given by integrable systems and toric manifolds.
In the latter case, the cohomology can be computed counting integral
points inside the associated Delzant polytope. In this article we extend
Kostant’s geometric quantization to semitoric integrable systems and
almost toric manifolds. In these cases the dimension of the acting torus
is smaller than half of the dimension of the manifold. In particular, we
compute the cohomology groups associated to the geometric quantization
if the real polarization is the one associated to an integrable system
with focus-focus type singularities in dimension four. As application
we determine models for the geometric quantization of K3 surfaces, a
spin-spin system, the spherical pendulum, and a spin-oscillator system
under this scheme.
2017-07-17T10:56:24ZMiranda Galcerán, EvaPresas, FranciscoSolha, RomeroKostant gave a model for the real geometric quantization
associated to polarizations via the cohomology associated to the sheaf of
flat sections of a pre-quantum line bundle. This model is well-adapted
for real polarizations given by integrable systems and toric manifolds.
In the latter case, the cohomology can be computed counting integral
points inside the associated Delzant polytope. In this article we extend
Kostant’s geometric quantization to semitoric integrable systems and
almost toric manifolds. In these cases the dimension of the acting torus
is smaller than half of the dimension of the manifold. In particular, we
compute the cohomology groups associated to the geometric quantization
if the real polarization is the one associated to an integrable system
with focus-focus type singularities in dimension four. As application
we determine models for the geometric quantization of K3 surfaces, a
spin-spin system, the spherical pendulum, and a spin-oscillator system
under this scheme.An invitation to singular symplectic geometry
http://hdl.handle.net/2117/106301
An invitation to singular symplectic geometry
Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Planas Bahí, Arnau; Oms, Cedric; Dempsey Bradell, Roisin Mary
In this paper we analyze in detail a collection of motivating examples to consider bm-
symplectic forms and folded-type symplectic structures. In particular, we provide models in
Celestial Mechanics for every bm-symplectic structure. At the end of the paper, we introduce
the odd-dimensional analogue to b-symplectic manifolds: b-contact manifolds.
2017-07-10T09:18:33ZMiranda Galcerán, EvaDelshams Valdés, AmadeuPlanas Bahí, ArnauOms, CedricDempsey Bradell, Roisin MaryIn this paper we analyze in detail a collection of motivating examples to consider bm-
symplectic forms and folded-type symplectic structures. In particular, we provide models in
Celestial Mechanics for every bm-symplectic structure. At the end of the paper, we introduce
the odd-dimensional analogue to b-symplectic manifolds: b-contact manifolds.