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We will show how to construct complex fields of transseries , which contain
,
an infinitely large variable
,
and which are closed under the field operations, infinite summation,
exponential and logarithm. Fields of complex transseries are valued
differential fields which have various interesting closure properties:
any differentially algebraic equation over
admits a solution in
, and
is Picard-Vessiot closed. An
interesting problem is to generalize Écalle's accelero-summation
theory to complex transseries.
Occasions: workshop on analyzable functions and applications, June 19, 2002
Documents: slideshow, TeXmacs source