Local theory of Fuchsian singular points
- Monodromy and holonomy.
- Growth of multivalued solutions.
- Tame singularities.
- Principal example: the Euler system , . Solution:
, monodromy , .
- Fuchsian condition.
- Gauge classification of linear systems, .
- Meromorphic gauge classification of tame (regular) systems.
- Holomorphic gauge classification of Fuchsian singularities: ,
, , .
- Resonances (integer differences between eigenvalues of .
- Holomorphic Eulerization of non-resonant Fuchsian singularities.
Reference: [IY], section 16.