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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeMar 24th 2010
   • PermaLink
   Author: zskoda
   Format: Markdown[[Fuchsian equation]]

   Fuchsian equation

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMar 24th 2010
   • (edited Mar 24th 2010)
   • PermaLink
   Author: zskoda
   Format: MarkdownStub [[Riemann-Hilbert correspondence]] and more references at [[meromorphic connection]], [[Stokes phenomenon]] , [[Riemann-Hilbert problem]], [[Hodge theory]].

   Stub Riemann-Hilbert correspondence and more references at meromorphic connection, Stokes phenomenon , Riemann-Hilbert problem, Hodge theory.

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeMar 25th 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownThe [[Stokes phenomenon]] does not happen to Fuchsian equations. Their formal meromorphic solutions are automatically convergent. Exactly the presence of the irregular singularities makes the appearance of formal solutions with zero radius of convergence. Now look around the origin. One can try to prove that there are asymptotic expressions at best in some regions of argument. There are jumps at certain slopes. In fact there is Stokes sheaf and the first nonabelian cohomology of the Stokes sheaf measures the obstruction for a formal meromomorphic expansion to be build up of sectorial true meromorphic expansions.

   The Stokes phenomenon does not happen to Fuchsian equations. Their formal meromorphic solutions are automatically convergent. Exactly the presence of the irregular singularities makes the appearance of formal solutions with zero radius of convergence. Now look around the origin. One can try to prove that there are asymptotic expressions at best in some regions of argument. There are jumps at certain slopes. In fact there is Stokes sheaf and the first nonabelian cohomology of the Stokes sheaf measures the obstruction for a formal meromomorphic expansion to be build up of sectorial true meromorphic expansions.