Finding invariant tori in the problem of a periodically corrugated waveguide
- Resource Type
- article
- Authors
- Rabelo, Adriano Fábio; Leonel, Edson D.
- Source
- Brazilian Journal of Physics. March 2008 38(1)
- Subject
- Chaos
Invariant Spanning Curves
Nonlinear Mappings
- Language
- English
- ISSN
- 0103-9733
Some dynamic properties for a light ray suffering specular reflections inside a periodically corrugated waveguide are studied. The dynamics of the model is described in terms of a two dimensional nonlinear area preserving map. We show that the phase space is mixed in the sense that there are KAM islands surrounded by a large chaotic sea that is confined by two invariant spanning curves. We have used a connection with the Standard Mapping near a transition from local to global chaos and found the position of these two invariant spanning curves limiting the size of the chaotic sea as function of the control parameter.