Local and global aspects of the qualitative theory of ordinary differential equations
Introduction to the qualitative theory of ordinary differential equations
On three-dimensional Reeb flows: implied existence of periodic orbits and a dynami...
| Full text | |
| Author(s): |
Buzzi, Claudio A.
;
Lamb, Jeroen S. W.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 5, n. 1, p. 51-66, Feb. 2005. |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics |
| Abstract | |
We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions. (AU) | |