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    Singular reduction of resonant Hamiltonians

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    Date
    2018
    Author
    Meyer, Kenneth Ray 
    Palacián Subiela, Jesús Francisco Upna
    Yanguas Sayas, Patricia Upna
    Version
    Acceso abierto / Sarbide irekia
    xmlui.dri2xhtml.METS-1.0.item-type
    Artículo / Artikulua
    Version
    Versión aceptada / Onetsi den bertsioa
    Project Identifier
    ES/6PN/MTM2011-28227 
    ES/1PE/MTM2014–59433 
    Impact
     
     
     
    10.1088/1361-6544/aab591
     
     
     
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    Abstract
    We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built u ... [++]
    We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built using normal forms and applying reduction theory obtaining the reduced Hamiltonian that is defined on the orbit space. Generically, the reduction is of singular character and we classify the singularities in the orbit space, getting three different types of singular points. A critical point of the reduced Hamiltonian corresponds to a family of periodic solutions in the full system whose characteristic multipliers are approximated accordingly to the nature of the critical point. [--]
    Subject
    Normal form and resonant Hamiltonian, Singular reduction, Cross section, Orbit space and orbifold, Plateau, Peak and ridge, Symplectic coordinates and symplectic smoothing
     
    Publisher
    IOP Publishing
     
    London Mathematical Society
     
    Published in
    Nonlinearity, vol. 31, n. 6
    Description
    This is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/aab591.
    Departament
    Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática / Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila / Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. InaMat - Institute for Advanced Materials
     
    Publisher version
    https://doi.org/10.1088/1361-6544/aab591
    URI
    https://hdl.handle.net/2454/28577
    Sponsorship
    The authors are partially supported by Projects MTM 2011-28227-C02-01 of the Ministry of Science and Innovation of Spain, MTM 2014-59433-C2-1-P of the Ministry of Economy and Competitiveness of Spain and by the Charles Phelps Taft Foundation.
    Appears in Collections
    • Artículos de revista DIMI - MIIS Aldizkari artikuluak [57]
    • Artículos de revista - Aldizkari artikuluak [2947]
    • Artículos de revista InaMat - InaMat aldizkari artikuluak [147]
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