Browsing by Author "Gonchenko, Marina"
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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 ... 
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 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 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 associated to 3D whiskered tori with cubic frequencies
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (201906)
External research report
Open AccessWe study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearlyintegrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3dimensional ... 
Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (20200101)
Article
Open AccessWe study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearlyintegrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3dimensional torus ... 
Homoclinic phenomena in conservative systems
Gonchenko, Marina (Universitat Politècnica de Catalunya, 20130429)
Doctoral thesis
Open AccessThe goal of this thesis is the study of homoclinic orbits in conservative systems (areapreserving maps and Hamiltonian systems). We consider homoclinic (biasymptotic) orbits either to saddle periodic orbits or to whiskered ... 
Mixed dynamics of twodimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
Lázaro Ochoa, José Tomás; Delshams Valdés, Amadeu; Gonchenko, Marina; Gonchenko, Sergey (American Institute of Mathematical Sciences, 201809)
Article
Open AccessWe study dynamics and bifurcations of 2dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure8). We ... 
On bifurcations of areapreserving and nonorientable maps with quadratic homoclinic tangencies
Delshams Valdés, Amadeu; Gonchenko, Marina (Springer, 2014)
Article
Open AccessWe study bifurcations of nonorientable areapreserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on nonorientable twodimensional surfaces. We consider one and twoparameter ... 
On bifurcations of homoclinic tangencies in areapreserving maps on nonorientable manifolds
Delshams Valdés, Amadeu; Gonchenko, Marina; Gonchenko, Sergey (Springer, 2016)
Part of book or chapter of book
Restricted access  publisher's policyWe study bifurcations of nonorientable areapreserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on nonorientable twodimensional manifolds. We consider one and two parameter ... 
On dynamics and bifurcations of areapreserving maps with homoclinic tangencies
Delshams Valdés, Amadeu; Gonchenko, Marina; Gonchenko, Sergey V. (20150901)
Article
Open AccessWe study bifurcations of areapreserving maps, both orientable (symplectic) and nonorientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to ... 
On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps
Gonchenko, Marina; Gonchenko, Sergey; Ovsyannikov, Ivan; Vieiro, Arturo (Institute of Physics (IOP), 20180430)
Article
Open AccessWe study the 1:4 resonance for the conservative cubic Hénon maps C^± with positive and negative cubic terms. These maps show up different bifurcation structures both for fixed points with eigenvalues¿±i and for 4periodic ... 
The dynamics of digits: calculating Pi with Galperin's billiards
Aretxabaleta, Xabier M.; Gonchenko, Marina; Harshman, Nathan L.; Jackson, Steven Glenn; Olshanii, Maxim; Astrakharchik, Grigori (Multidisciplinary Digital Publishing Institute (MDPI), 20200401)
Article
Open AccessIn Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number p . This classical, onedimensional threebody system (counting the hard wall) calculates the digits of p ...