An energy-momentum map for the time-reversal symmetric 1:1 resonance with Z2 x Z2 symmetry

PHYSICA D-NONLINEAR PHENOMENA

卷:271

Article

Pucacco, Giuseppe^1,2  Marchesiello, Antonella³ 

[1] Univ Roma Tor Vergata, Dipartimento Fis, I-00133 Rome, Italy

[2] Univ Roma Tor Vergata, Ist Nazl Fis Nucl, Sez Roma 2, I-00133 Rome, Italy

[3] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Decin Branch, Decin 40501, Czech Republic

关键词: Finite-dimensional Hamiltonian systems;    Perturbation theory;    Normal forms;   

DOI  :  10.1016/j.physd.2013.12.009

来源: Elsevier

【 摘 要 】

We present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1:1 resonant Hamiltonian normal forms invariant under Z(2) x Z(2) symmetry. The rich structure of these classical systems is investigated both with a singularity theory approach and geometric methods. The geometric approach readily allows to find an energy-momentum map describing the phase space structure of each member of the family and a catastrophe map that captures its global features. Quadrature formulas for the actions, periods and rotation number are also provided. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free