Supplying an simple advent to analytic continuation and monodromy, the 1st a part of this quantity applies those notions to the neighborhood and worldwide learn of complicated 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 perspective.
the second one half expounds 1-summability and Ecalle’s conception of resurgence lower than quite basic stipulations. It includes a number of examples and offers an research of the singularities within the Borel aircraft through “alien calculus”, which gives an entire description of the Stokes phenomenon for linear or non-linear differential or distinction equations.
the 1st of a sequence of 3, entitled Divergent sequence, Summability and Resurgence, this quantity is geared toward graduate scholars, mathematicians and theoretical physicists drawn to geometric, algebraic or neighborhood analytic homes of dynamical platforms. It comprises important workouts with options. the necessities are a operating wisdom of basic complicated research and differential algebra.
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