Topological construction of transseries and introduction to generalized Borel summability

Details Topological construction of transseries and introduction to generalized Borel summability Topological construction of transseries and introduction to generalized Borel summability

2006-08-13

arxiv.org/abs/math/0608309v1

AMS CONM series vol. 373, 137--177, 2005

Mathematics

Classical Analysis and ODEs

Scientific paper

Transseries in the sense of \'Ecalle are constructed using a topological approach. A general contractive mapping principle is formulated and proved, showing the closure of transseries under a wide class of operations. In the second part we give an overview of results and methods reconstruction of actual functions and solutions of equations from transseries by generalized Borel summation with in ordinary and partial differential and difference equations.

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