A NORMALLY ELLIPTIC HAMILTONIAN BIFURCATION

Authors
BROER HW CHOW SN KIM Y VEGTER G
Citation
Hw. Broer et al., A NORMALLY ELLIPTIC HAMILTONIAN BIFURCATION, Zeitschrift fur angewandte Mathematik und Physik, 44(3), 1993, pp. 389-432
Citations number
51
Categorie Soggetti
Mathematics,"Mathematical Method, Physical Science",Mathematics
Journal title
Zeitschrift fur angewandte Mathematik und Physik → ACNP
ISSN journal
00442275
Volume
44
Issue
3
Year of publication
1993
Pages
389 - 432
Database
ISI
SICI code
0044-2275(1993)44:3<389:ANEHB>2.0.ZU;2-I
Abstract
A universal local bifurcation analysis is presented of an autonomous H amiltonian system around a certain equilibrium point. This central equ ilibrium has a double zero eigenvalue, the other eigenvalues being in general position. Main emphasis is given to the 2 degrees of freedom c ase where these other eigenvalues are purely imaginary. By normal form techniques and Singularity Theory unfoldings are obtained. having 'in tegrable' approximations related to the Elliptic and Hyperbolic Umbili c Catastrophes.