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math.DS2020
Iterations and groups of formal transformations
O. V. Kaptsov
In this paper, we consider the problem of formal iteration. We construct an area preserving mapping which does not have any square root. This leads to a counterexample to Moser's e…
math.DS2016
Ideals of partial differential equations
Oleg V. Kaptsov
We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gröbner ba…