On the singularity structure of invariant curves of symplectic mappings.

Abstract

We study invariant curves in standard-like maps conjugate to rigid rotation with complex frequencies. The main goal is to study the analyticity domain of the functions defined perturbatively by Lindstedt perturbation expansions. We argue, based on infinite-dimensional bifurcation theory that the boundary of analyticity should typically consist of branch points of order two and we verify it in some examples using nonperturbative numerical methods. We show that this nature of the singularities of the analyticity domain can explain previously reported numerical results and also suggests other numerical methods. (c) 1995 American Institute of Physics.