Browsing by Author "Delshams Valdés, Amadeu"
Now showing items 21-40 of 93
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CÀLCUL II (Examen de reavaluació 2n quadrimestre)
(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)
(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
(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
(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
(2023-04)
Article
Open Access -
Effective stability and KAM theory
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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 ...
