A method for the numerical computation of invariant circles of maps is presented, along with appropriate techniques for its implementation. The method involves solution of a functional equation by discretization and Newton iteration. The resulting algorithm is applied to a map of the cylinder and some examples of bifurcations of invariant circles are illustrated. Generalization of the method to the computation of invariant circles in more than two dimensions as well as sections of invariant tori is discussed.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics