Formal Normal Forms and Realization Theorems for Difference Systems

Student: Merzliakov Alexey

Educational Programme: Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2019

The text of the paper raises questions about finding a formal solution for a maximally generalized system of equations (where each equation bounds two points z and \varphi(z), where \varphi (z) is an automorphism). It turns out that some techniques for constructing a formal solution of an ODE system can be easily transferred for this case. Also, an approximate plan for proving a positive response to the monodromy problem for the case of a system of difference equations will be described in the second part of the work, namely, it will be shown that the system can be reconstructed from a known monodromy matrix.

Full text (added June 3, 2019)

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