Instead it introduces complexification of the original problem, and develops a generalization of the theory of normally hyperbolic invariant curves and stable manifolds, which allow the use of global methods of complex analysis.
Instead it introduces a complexification of the original problem, and develops a generalization of the theory of normally hyperbolic invariant curves and stable manifolds to multi-valued maps F:\\ mathbb ^ 2\\ to\\ mathbb ^ 2. This method allows the use of global methods of complex analysis.