DSpace Collection:
http://hdl.handle.net/2117/5340
Wed, 01 Apr 2015 08:17:37 GMT2015-04-01T08:17:37Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoNon-integrability of measure preserving maps via Lie symmetries
http://hdl.handle.net/2117/26843
Title: Non-integrability of measure preserving maps via Lie symmetries
Authors: Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Abstract: We consider the problem of characterizing, for certain natural
number m, the local C^m-non-integrability near
elliptic fixed points of smooth planar measure preserving maps. Our
criterion relates this non-integrability with the existence of some
Lie Symmetries associated to the maps, together with the study of
the finiteness of its periodic points. One of the steps in the proof
uses the regularity of the period function on the whole period
annulus for non-degenerate centers, question that we believe that is
interesting by itself. The obtained criterion can be applied to
prove the local non-integrability of the Cohen map and of several
rational maps coming from second order difference equations.
Description: Preprint.Thu, 19 Mar 2015 12:49:35 GMThttp://hdl.handle.net/2117/268432015-03-19T12:49:35ZCima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, VíctornoIntegrability and non-integrability of
maps, Measure preserving maps, Lie symmetries, Integrable vector
fields, Period function, Isochronous centers, Cohen map, Difference
equations.We consider the problem of characterizing, for certain natural
number m, the local C^m-non-integrability near
elliptic fixed points of smooth planar measure preserving maps. Our
criterion relates this non-integrability with the existence of some
Lie Symmetries associated to the maps, together with the study of
the finiteness of its periodic points. One of the steps in the proof
uses the regularity of the period function on the whole period
annulus for non-degenerate centers, question that we believe that is
interesting by itself. The obtained criterion can be applied to
prove the local non-integrability of the Cohen map and of several
rational maps coming from second order difference equations.Singular solutions for a class of traveling wave equations arising in hydrodynamics
http://hdl.handle.net/2117/26450
Title: Singular solutions for a class of traveling wave equations arising in hydrodynamics
Authors: Geyer, Anna; Mañosa Fernández, Víctor
Abstract: We give an exhaustive characterization of singular weak solutions for ordinary
differential equations of the form $\ddot{u}\,u +
\frac{1}{2}\dot{u}^2 + F'(u) =0$, where $F$ is an analytic function.
Our motivation stems from the fact that in the context of hydrodynamics several
prominent equations are reducible to an equation of this form
upon passing to a moving frame. We construct peaked and cusped waves,
fronts with finite-time decay and compact solitary waves. We prove
that one cannot obtain peaked and compactly supported traveling waves for the
same equation. In particular, a peaked traveling wave cannot have compact
support and vice versa. To exemplify the approach we apply our
results to the Camassa-Holm equation and the equation for surface waves
of moderate amplitude, and show how the different types of singular solutions
can be obtained varying the energy level of the corresponding planar Hamiltonian systems.
Description: PreprintFri, 20 Feb 2015 13:24:49 GMThttp://hdl.handle.net/2117/264502015-02-20T13:24:49ZGeyer, Anna; Mañosa Fernández, VíctornoCamassa-Holm equation, integrable vector fields, singular ordinary differential equations, traveling waves.We give an exhaustive characterization of singular weak solutions for ordinary
differential equations of the form $\ddot{u}\,u +
\frac{1}{2}\dot{u}^2 + F'(u) =0$, where $F$ is an analytic function.
Our motivation stems from the fact that in the context of hydrodynamics several
prominent equations are reducible to an equation of this form
upon passing to a moving frame. We construct peaked and cusped waves,
fronts with finite-time decay and compact solitary waves. We prove
that one cannot obtain peaked and compactly supported traveling waves for the
same equation. In particular, a peaked traveling wave cannot have compact
support and vice versa. To exemplify the approach we apply our
results to the Camassa-Holm equation and the equation for surface waves
of moderate amplitude, and show how the different types of singular solutions
can be obtained varying the energy level of the corresponding planar Hamiltonian systems.Lie symmetries of birational maps preserving genus 0 fibrations
http://hdl.handle.net/2117/26449
Title: Lie symmetries of birational maps preserving genus 0 fibrations
Authors: Llorens, Mireia; Mañosa Fernández, Víctor
Abstract: We prove that any planar birational integrable map, which preserves
a fibration given by genus $0$ curves has a Lie symmetry and some
associated invariant measures. The obtained results allow to study
in a systematic way the global dynamics of these maps. Using this
approach, the dynamics of several maps is described. In particular
we are able to give, for particular examples, the explicit
expression of the rotation number function, and the set of periods
of the considered maps.
Description: Preprint.Fri, 20 Feb 2015 12:54:58 GMThttp://hdl.handle.net/2117/264492015-02-20T12:54:58ZLlorens, Mireia; Mañosa Fernández, VíctornoIntegrable maps, Lie symmetries, Periodic
orbits, Rational parameterizations.We prove that any planar birational integrable map, which preserves
a fibration given by genus $0$ curves has a Lie symmetry and some
associated invariant measures. The obtained results allow to study
in a systematic way the global dynamics of these maps. Using this
approach, the dynamics of several maps is described. In particular
we are able to give, for particular examples, the explicit
expression of the rotation number function, and the set of periods
of the considered maps.Periodic orbits of planar integrable birational maps
http://hdl.handle.net/2117/21748
Title: Periodic orbits of planar integrable birational maps
Authors: Gálvez Carrillo, Maria Immaculada; Mañosa Fernández, Víctor
Abstract: A birational planar map F possessing a rational ﬁrst integral preserves a
foliation of the plane given by algebraic curves which, if F is not globally periodic,
is given by a foliation of curves that have generically genus 0 or 1. In the genus 1
case, the group structure of the foliation characterizes the dynamics of any birational
map preserving it. We will see how to take advantage of this structure to ﬁnd periodic
orbits of such maps.Tue, 25 Feb 2014 12:09:41 GMThttp://hdl.handle.net/2117/217482014-02-25T12:09:41ZGálvez Carrillo, Maria Immaculada; Mañosa Fernández, VíctornoDiscrete dynamical systems, Algebraic geometry, Birational maps, Integrable maps, Elliptic curves, Periodic orbits.A birational planar map F possessing a rational ﬁrst integral preserves a
foliation of the plane given by algebraic curves which, if F is not globally periodic,
is given by a foliation of curves that have generically genus 0 or 1. In the genus 1
case, the group structure of the foliation characterizes the dynamics of any birational
map preserving it. We will see how to take advantage of this structure to ﬁnd periodic
orbits of such maps.Basin of attraction of triangular maps with applications
http://hdl.handle.net/2117/20131
Title: Basin of attraction of triangular maps with applications
Authors: Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Abstract: We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or 2-periodic points. Finally, we apply our results to a variety of examples, from particular cases of triangular systems to some planar quasi-homogeneous maps, and some multiplicative and additive difference equations, as well.
Description: PreprintFri, 13 Sep 2013 10:48:34 GMThttp://hdl.handle.net/2117/201312013-09-13T10:48:34ZCima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, VíctornoAttractors, Periodic Orbits, Triangular Maps, Discrete Dynamical Systems, Quasi-homogeneous Maps.We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or 2-periodic points. Finally, we apply our results to a variety of examples, from particular cases of triangular systems to some planar quasi-homogeneous maps, and some multiplicative and additive difference equations, as well.Different approaches to the global periodicity problem
http://hdl.handle.net/2117/20123
Title: Different approaches to the global periodicity problem
Authors: Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor; Mañosas, Francesc
Abstract: t Let F be a real or complex n-dimensional map. It is said that F is globally
periodic if there exists some p ∈ N
+ such that Fp(x) = x for all x, where F
k = F ◦ F k−1, k ≥ 2. The minimal p satisfying this property is called the period of F. Given a m-dimensional parametric family of maps, say Fλ, a problem of current interest is to determine all the values of λ such that Fλ is globally periodic, together with their corresponding periods. The aim of this paper is to show some techniques that we
use to face this question, as well as some recent results that we have obtained. We
will focus on proving the equivalence of the problem with the complete integrability
of the dynamical system induced by the map F, and related issues; on the use of the
local linearization given by the Bochner Theorem; and on the use the Normal Form
theory. We also present some open questions in this setting.
Description: PreprintThu, 12 Sep 2013 12:19:54 GMThttp://hdl.handle.net/2117/201232013-09-12T12:19:54ZCima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor; Mañosas, FrancescnoGlobally periodic maps. Periodic orbits.t Let F be a real or complex n-dimensional map. It is said that F is globally
periodic if there exists some p ∈ N
+ such that Fp(x) = x for all x, where F
k = F ◦ F k−1, k ≥ 2. The minimal p satisfying this property is called the period of F. Given a m-dimensional parametric family of maps, say Fλ, a problem of current interest is to determine all the values of λ such that Fλ is globally periodic, together with their corresponding periods. The aim of this paper is to show some techniques that we
use to face this question, as well as some recent results that we have obtained. We
will focus on proving the equivalence of the problem with the complete integrability
of the dynamical system induced by the map F, and related issues; on the use of the
local linearization given by the Bochner Theorem; and on the use the Normal Form
theory. We also present some open questions in this setting.On the set of periods of the 2-periodic Lyness’ Equation
http://hdl.handle.net/2117/20122
Title: On the set of periods of the 2-periodic Lyness’ Equation
Authors: Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
Abstract: We study the periodic solutions of the non–autonomous periodic Lyness’ recurrence un+2 = (an +un+1)=un, where fangn is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a;b) 6= (1;1), then there exists a value p0(a;b) such that for any p > p0(a;b) there exist continua of initial conditions giving rise to 2p–periodic sequences. (2) The set of minimal periods arising when (a;b) 2 (0;¥) 2 and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a 6= b, then it does not appear any odd period, except 1.
Description: PreprintThu, 12 Sep 2013 11:54:40 GMThttp://hdl.handle.net/2117/201222013-09-12T11:54:40ZBastien, Guy; Mañosa Fernández, Víctor; Rogalski, MarcnoPeriodic Orbits, Difference equations, QRT maps, Integrable systems.We study the periodic solutions of the non–autonomous periodic Lyness’ recurrence un+2 = (an +un+1)=un, where fangn is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a;b) 6= (1;1), then there exists a value p0(a;b) such that for any p > p0(a;b) there exist continua of initial conditions giving rise to 2p–periodic sequences. (2) The set of minimal periods arising when (a;b) 2 (0;¥) 2 and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a 6= b, then it does not appear any odd period, except 1.Periodic orbits of planar integrable birational maps
http://hdl.handle.net/2117/20107
Title: Periodic orbits of planar integrable birational maps
Authors: Mañosa Fernández, Víctor
Abstract: Conferència convidada al congrés NOMA'13.Mon, 09 Sep 2013 08:45:00 GMThttp://hdl.handle.net/2117/201072013-09-09T08:45:00ZMañosa Fernández, VíctornoPeriodic orbits, birational maps, integrability, nonlinear dynamics, elliptic curves.Conferència convidada al congrés NOMA'13.Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations
http://hdl.handle.net/2117/19168
Title: Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations
Authors: Juher Barrot, David; Mañosa Fernández, Víctor
Abstract: We consider the spread of an infectious disease on a heterogeneous metapopulation
deﬁned by any (correlated or uncorrelated) network. The infection evolves under transmission, recovering and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufﬁcient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks
Description: Preprint version of the paperMon, 13 May 2013 08:19:06 GMThttp://hdl.handle.net/2117/191682013-05-13T08:19:06ZJuher Barrot, David; Mañosa Fernández, VíctornoSIS epidemics, Complex networks, Spectral properties, Connectivity matrix, Disease-free equilibrium.We consider the spread of an infectious disease on a heterogeneous metapopulation
deﬁned by any (correlated or uncorrelated) network. The infection evolves under transmission, recovering and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufﬁcient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networksNon autonomous 2-periodic Gumovski-Mira difference equations
http://hdl.handle.net/2117/12720
Title: Non autonomous 2-periodic Gumovski-Mira difference equations
Authors: Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Abstract: We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ones di er dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.Tue, 07 Jun 2011 11:53:42 GMThttp://hdl.handle.net/2117/127202011-06-07T11:53:42ZCima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, VíctornoIntegrable and chaotic difference equations and maps, Rational difference equations with periodic coefficients, Perturbed twist mapsWe consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ones di er dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.The hydraulic influence matrix of opening gate trajectories in canals based on the method of characteristics: concept, compilation and practical examples
http://hdl.handle.net/2117/12473
Title: The hydraulic influence matrix of opening gate trajectories in canals based on the method of characteristics: concept, compilation and practical examples
Authors: Soler Guitart, Joan; Gómez, Manuel; Rodellar Benedé, JoséThu, 05 May 2011 10:53:13 GMThttp://hdl.handle.net/2117/124732011-05-05T10:53:13ZSoler Guitart, Joan; Gómez, Manuel; Rodellar Benedé, JosénoDesigualtats matricials útils en control robust
http://hdl.handle.net/2117/12085
Title: Desigualtats matricials útils en control robust
Authors: Rubió Massegú, Josep; Palacios Quiñonero, Francisco; Rossell Garriga, Josep Maria
Abstract: En aquest treball presentem un recull de les desigualtats matricials més freqüentment utilitzades en el context del control robust amb possibles retardaments, a temps continu o discret. Juntament amb les demostracions de les desigualtats, també s'inclou una breu descripció d'altres materials d'interès, com són els complements de Schur i la fórmula de Sherman-Morrison-Woodbury.Fri, 25 Mar 2011 16:33:00 GMThttp://hdl.handle.net/2117/120852011-03-25T16:33:00ZRubió Massegú, Josep; Palacios Quiñonero, Francisco; Rossell Garriga, Josep MarianoEn aquest treball presentem un recull de les desigualtats matricials més freqüentment utilitzades en el context del control robust amb possibles retardaments, a temps continu o discret. Juntament amb les demostracions de les desigualtats, també s'inclou una breu descripció d'altres materials d'interès, com són els complements de Schur i la fórmula de Sherman-Morrison-Woodbury.On two and three periodic Lyness difference equations
http://hdl.handle.net/2117/6893
Title: On two and three periodic Lyness difference equations
Authors: Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Abstract: We describe the sequences {x_n}_n given by the non-autonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x_1,x_2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations.Fri, 09 Apr 2010 11:12:00 GMThttp://hdl.handle.net/2117/68932010-04-09T11:12:00ZCima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, VíctornoDifference equations with periodic coefficients, Circle maps, Rotation numberWe describe the sequences {x_n}_n given by the non-autonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x_1,x_2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations.