Browsing by Author "Gutiérrez Serrés, Pere"

A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (201407)
External research report
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 (201409)
External research report
Open AccessWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearlyintegrable 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, 201411)
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 ... 
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 ... 
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 ... 
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 (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 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 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. ... 
Homoclinic orbits to invariant tori in Hamiltonian systems
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (1998)
Article
Open AccessWe consider a perturbation of an integrable Hamiltonian system which possesses invariant tori with coincident whiskers (like some rotators and a pendulum). Our goal is to measure the splitting distance between the perturbed ... 
Homoclinic orbits to invariant tori near a homoclinic orbit to centercentersaddle equilibrium
Koltsova, Oksana; Lerman, L. M. (Lev M.); Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (2003)
Article
Open AccessWe consider a perturbation of an integrable Hamiltonian vector field with three degrees of freedom with a center–center–saddle equilibrium having a homoclinic orbit or loop. With the help of a Poincaré map (chosen based ... 
Splitting and melnikov potentials in hamiltonian systems
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (2000)
Article
Open Access 
Splitting potential and PoincaréMelnikov method for whiskered tori in Hamiltonian Systems
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (1999)
Article
Open AccessWe deal with a perturbation of a hyperbolic integrable Hamiltonian system with n+1 degrees of freedom. The integrable system is assumed to have ndimensional hyperbolic invariant tori with coincident whiskers (separatric ... 
Transversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the HamiltonJacobi equation
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere; Pacha Andújar, Juan Ramón (2011)
External research report
Open AccessWe consider a Hamiltonian system with 2 degrees of freedom, with a hyperbolic equilibrium point having a loop or homoclinic orbit (or, alternatively, two hyperbolic equilibrium points connected by a heteroclinic orbit), ... 
Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the HamiltonJacobi equation
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere; Pacha Andújar, Juan Ramón (201207)
External research report
Open AccessThe key point of our approach is to write the invariant manifolds in terms of generating functions, which are solutions of the HamiltonJacobi equation. In some examples, we show that it is enough to analyse the phase ...