Divergent Series, Summability and Resurgence I-III

Features a thorough resurgent analysis of the celebrated non-linear differential equation Painlevé I Includes new specialized results in the theory of resurgence For the first time, higher order Stokes phenomena of Painlevé I are made explicit by means of the so-called bridge equation Features an elementary, self-contained introduction to analytic differential Galois theory and the Riemann-Hilbert problem. Provides a foundation that will allow the reader to independently explore and understand the specialized literature in the field. For the first time, resurgence theory is introduced with great pedagogical care and the main proofs are given in full detail. Can be treated both as a reference book and as a tutorial on the theories of summability and their links to the formal and local analytic aspects of linear ordinary differential equations.