On the analytic structure of two-degree-of-freedom Hamiltonian systems around an elliptic fixed point

Tassos C. Bountis, Vassilios M. Rothos

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It has been proved by Ziglin, for a large class of two-degree-of-freedom (2DOF) Hamiltonian systems, that transverse intersections of the invariant manifolds of saddle fixed points imply infinite branching of solutions in the complex time plane and the non-existence of a second analytic integral of the motion. Here, we follow a similar approach to show the existence of infinitely sheeted solutions for 2DOF. Hamiltonians which exhibit, upon perturbation, subharmonic bifurcations of resonant tori around an elliptic fixed point. Moreover, as shown recently, these Hamiltonian systems are non-integrable if their resonant tori form a dense set.

Original languageEnglish
Pages (from-to)877-886
Number of pages10
JournalNonlinearity
Volume9
Issue number4
DOIs
Publication statusPublished - 1996
Externally publishedYes

Fingerprint

Hamiltonians
Hamiltonian Systems
Torus
degrees of freedom
Degree of freedom
Fixed point
Subharmonics
saddles
Invariant Manifolds
Saddlepoint
intersections
Nonexistence
Branching
Transverse
Bifurcation (mathematics)
Bifurcation
Intersection
Perturbation
Imply
perturbation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

On the analytic structure of two-degree-of-freedom Hamiltonian systems around an elliptic fixed point. / Bountis, Tassos C.; Rothos, Vassilios M.

In: Nonlinearity, Vol. 9, No. 4, 1996, p. 877-886.

Research output: Contribution to journalArticle

Bountis, Tassos C. ; Rothos, Vassilios M. / On the analytic structure of two-degree-of-freedom Hamiltonian systems around an elliptic fixed point. In: Nonlinearity. 1996 ; Vol. 9, No. 4. pp. 877-886.
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