Resurgent functions and splitting problems

Understand

The present text is an introduction to \'Ecalle's theory of resurgent functions and alien calculus, in connection with problems of exponentially small separatrix splitting.

• An outline of the resurgent treatment of Abel's equation for resonant dynamics in one complex variable is included.
• The emphasis is on examples of nonlinear difference equations, as a simple and natural way of introducing the concepts.