Browsing by Author "Delshams Valdés, Amadeu"
Now showing items 21-40 of 93
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CÀLCUL II (Examen de reavaluació 2n quadrimestre)
Fedorov, Yuri; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi; Delshams Valdés, Amadeu; Martín, Ferran; Coltraro, Franco; Limón, Antonio; Orobitg, Pol (Universitat Politècnica de Catalunya, 2024-07-05)
Exam
Restricted access to the UPC academic community -
Consideracions al voltant de la Funció Beta a l’obra de Leonhard Euler (1707-1783)
Delshams Valdés, Amadeu; Massa Esteve, Maria Rosa (Centre de recerca per a la Història de la Tècnica "Francesc Santponç i Roca". Escola Tècnica Superior d'Enginyeria Industrial de Barcelona (Universitat Politècnica de Catalunya). Càtedra UNESCO de Tècnica i Cultura de la UPC, 2008)
Article
Open Access -
Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (2014-09)
Research report
Open AccessWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider ... -
Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (Springer, 2014-11)
Article
Open AccessWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We ... -
Correction to: exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere; Gonchenko, Marina (2023-04)
Article
Open Access -
Effective stability and KAM theory
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (1995)
Article
Open AccessThe two main stability results for nearly integrable Hamiltonian systems are revisited: Nekhoroshev theorem, concerning exponential lower bounds for the stability time (effective stability), and KAM theorem, concerning ... -
Effective stability in reversible systems
Delshams Valdés, Amadeu; Lázaro Ochoa, José Tomás (1997)
Article
Open AccessIn this paper we present a procedure to put in normal form a nearly-integrable reversible system, not necessarily a Hamiltonian system. Furthermore, non-resonant stability estimates are obtained. As an application we discuss ... -
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 (2009-03)
Article
Restricted access - publisher's policyBeta integrals for several non-integer 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 non-integrable 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 non-integrable systems on singular symplectic manifolds
Delshams Valdés, Amadeu; Miranda Galcerán, Eva; Kiesenhofer, Anna (2016-12)
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)
Research report
Open AccessWe study the splitting of invariant manifolds of whiskered t ori with two or three frequencies in nearly-integrable Hamiltonian systems. We consider 2-dimensional 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 (2014-01-01)
Article
Open AccessWe study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional 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 (2014-02)
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 2-dimensional 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 nearly-integrable Hamiltonian near a simple resonance. The model consists of an integrable ... -
Exponentially small splitting for whiskered tori in Hamiltonian systems: Flow-box coordinates and upper bounds
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere; Martínez-Seara 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 nearly-integrable 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 (2016-06)
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)
Research report
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. -
Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (2019-06)
Research report
Open AccessWe study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional ...