Delivering an common creation to analytic continuation and monodromy, the 1st a part of this quantity applies those notions to the neighborhood and international research of advanced linear differential equations, their formal strategies at singular issues, their monodromy and their differential Galois teams. The Riemann-Hilbert challenge is mentioned from Bolibrukh’s viewpoint.
the second one half expounds 1-summability and Ecalle’s concept of resurgence lower than particularly basic stipulations. It includes a variety of examples and offers an research of the singularities within the Borel aircraft through “alien calculus”, which supplies a whole description of the Stokes phenomenon for linear or non-linear differential or distinction equations.
the 1st of a chain of 3, entitled Divergent sequence, Summability and Resurgence, this quantity is aimed toward graduate scholars, mathematicians and theoretical physicists drawn to geometric, algebraic or neighborhood analytic homes of dynamical structures. It contains important workouts with recommendations. the necessities are a operating wisdom of effortless complicated research and differential algebra.
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