Browsing by Author "Delshams Valdés, Amadeu"

Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (1996)
Article
Open AccessWe give a precise statement for KAM theorem in a neighbourhood of an elliptic equilibrium point of a Hamiltonian system. If the frequencies of the elliptic point are nonresonant up to a certain order $K\ge4$, and a ... 
Euler's beta integral in Pietro Mengoli's works
Massa Esteve, Maria Rosa; Delshams Valdés, Amadeu (200903)
Article
Restricted access  publisher's policyBeta integrals for several noninteger values of the exponents were calculated by Leonhard Euler in 1730, when he was trying to find the general term for the factorial function by means of an algebraic expression. ... 
Examples of integrable and nonintegrable systems on singular symplectic manifolds
Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Kiesenhoferb, Anna (2016)
Article
Open AccessWe present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell’s ... 
Examples of integrable and nonintegrable systems on singular symplectic manifolds
Delshams Valdés, Amadeu; Miranda Galcerán, Eva; Kiesenhofer, Anna (201612)
External research report
Open AccessWe present a collection of examples borrowed from celes tial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization trans formations, Appell's ... 
Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (2013)
External research report
Open AccessWe study the splitting of invariant manifolds of whiskered t ori with two or three frequencies in nearlyintegrable Hamiltonian systems. We consider 2dimensional tori with a frequency vector ω = (1 , Ω) where Ω is ... 
Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (20140101)
Article
Open AccessWe study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2dimensional torus ... 
Exponentially small estimates for KAM theorem near an elliptic equilibrium point
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (1997)
Article
Open AccessWe give a precise statement of KAM theorem for a Hamiltonian system in a neighborhood of an elliptic equilibrium point. If the frequencies of the elliptic point satisfy a Diophantine condition, with exponent $\tau$, and ... 
Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (201402)
External research report
Open AccessWe study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2dimensional torus with ... 
Exponentially small splitting for whiskered tori in Hamiltonian systems: Continuation of transverse homoclinic orbits
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (2003)
Article
Open AccessWe consider an example of singular or weakly hyperbolic Hamiltonian, with 3 degrees of freedom, as a model for the behaviour of a nearlyintegrable Hamiltonian near a simple resonance. The model consists of an integrable ... 
Exponentially small splitting for whiskered tori in Hamiltonian systems: Flowbox coordinates and upper bounds
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere; MartínezSeara Alonso, M. Teresa (2003)
Article
Open AccessWe consider a singular or weakly hyperbolic Hamiltonian, with $n+1$ degrees of freedom, as a model for the behaviour of a nearlyintegrable Hamiltonian near a simple resonance. The model consists of an integrable Hamiltonian ... 
Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (201606)
Article
Open AccessThe splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. We consider a torus with a fast ... 
Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (2015)
External research report
Open AccessThe splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearlyintegrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. 
Exponentially small splitting of separatrices for perturbed integrable standardlike maps
Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
Article
Open AccessWe consider fast quasiperiodic perturbations with two frequencies $(1/\varepsilon,\gamma/\varepsilon)$ of a pendulum, where $\gamma$ is the golden mean number. The complete system has a twodimensional invariant ... 
Exponentially small splitting of separatrices for whiskered tori in Hamiltonian systems
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (2003)
Article
Open AccessWe study the existence of transverse homoclinic orbits in a singular or weakly hyperbolic Hamiltonian, with $3$ degrees of freedom, as a model for the behaviour of a nearlyintegrable Hamiltonian near a simple resonance. ... 
Exponentially small splitting of separatrices under fast quasiperiodic forcing
Delshams Valdés, Amadeu; Gelfreich, Vassili; Jorba, Angel; MartínezSeara Alonso, M. Teresa (1997)
Article
Open AccessWe consider fast quasiperiodic perturbations with two frequencies $(1/\varepsilon,\gamma/\varepsilon)$ of a pendulum, where $\gamma$ is the golden mean number. The complete system has a twodimensional invariant ... 
Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems
Delshams Valdés, Amadeu; Huguet Casades, Gemma (20081208)
Article
Open AccessIn the present paper we consider the case of a general $\cont{r+2}$ perturbation, for $r$ large enough, of an a priori unstable Hamiltonian system of $2+1/2$ degrees of freedom, and we provide explicit conditions on it, ... 
Geometric properties of the scattering map of a normally hyperbolic invariant manifold
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; Seara, Tere M. (Elsevier, 2008)
Article
Open AccessGiven a normally hyperbolic invariant manifold Λ for a map f , whose stable and unstable invariant manifolds intersect transversally, we consider its associated scattering map. That is, the map that, given an asymptotic ... 
Geometric properties of the scattering map of a normally hyperbolic invariant manifold
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; Seara, Tere M. (20061010)
Article
Open AccessGiven a normally hyperbolic invariant manifold $\Lambda$ for a map $f$, whose stable and unstable invariant manifolds intersect transversally, we consider its associated scattering map. That is, the map that, given an ... 
Global instability in the restricted planar elliptic three body problem
Delshams Valdés, Amadeu; Kaloshin, Vadim; Rosa Ibarra, Abraham de la (20180101)
Article
Restricted access  publisher's policyThe restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet or an asteroid) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) ... 
Homoclinic billiard orbits inside symmetrically perturbed ellipsoids
Delshams Valdés, Amadeu; Fedorov, Yuri; Ramírez Ros, Rafael (2000)
Article
Open AccessThe billiard motion inside an ellipsoid of ${\bf R}^{3}$ is completely integrable. If the ellipsoid is not of revolution, there are many orbits biasymptotic to its major axis. The set of biasymptotic orbits is described ...