Are there Irregular Families of Characteristic Curves?

  • Joaquim Font
  • Carles Simó
Part of the NATO ASI Series book series (NSSB, volume 272)


For Hamiltonian systems of two degrees of freedom the symmetric periodic orbits of a given type appear in continuous families. Every periodic orbit can be represented by one point in some suitable plane of parameters, and the full family is represented by the so called characteristic curve. Some of these curves have components which are isolated, and they are called irregular characteristic curves. In this work we consider one of the examples of this kind of behaviour and we show that if we embed the given Hamiltonian in a one parameter family the components are no longer isolated. Furthermore we give a full explanation of the structure and evolution of those characteristic curves, by using several invariant manifolds.


Periodic Orbit Hamiltonian System Invariant Manifold Parameter Family Characteristic Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Barbanis, B.: Celestial Mechanics 33 (1984) 385.ADSMATHCrossRefGoogle Scholar
  2. [2]
    Barbanis, B.: Celestial Mechanics 36 (1985) 257.MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    Barbanis, B.: Celestial Mechanics 39 (1986) 345.MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    Contopoulos, G.: Astrophysical Journal 138 (1963) 1297.MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    Font, J.: The role of homoclinic and heteroclinic orbits in two-degrees of freedom Hamiltonian systems (1990), PhD Thesis. University of Barcelona.Google Scholar
  6. [6]
    Font, J. and Grau, M.: Proc. NATO-ASI Series C vol. 246 (1988) 385.MathSciNetGoogle Scholar
  7. [7]
    Font, J. and Simó, C.: CEDYA Universidad de Santander (1985) (to appear).Google Scholar
  8. [8]
    Font, J. and Simó, C.: European Conference on Iteration Theory (ECIT 87) World Scientific (1989) 421.Google Scholar
  9. [9]
    Font, J. and Simó, C.: Spirals and bubbles in characteristic curves of periodic orbits, in preparation.Google Scholar
  10. [10]
    Moser, J.K.: Comm. Pure and Appl. Math. XI (1958) 257.CrossRefGoogle Scholar
  11. [11]
    Simó, C.: Homoclinic and heteroclinic phenomena in some Hamiltonian systems in Hamiltonian Dynamical systems, ed. K.R. Meyer and D.G. Saari, Contemporary Mathematics 81 (1988) 193.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Joaquim Font
    • 1
  • Carles Simó
    • 1
  1. 1.Departament de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations