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Local and global branching of solutions of differential equations

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CATW01 - The complex analysis toolbox: new techniques and perspectives

We will consider differential equations with movable branch points in the complex domain.  We will describe families of equations for which we can prove that the only movable singularities of solutions are algebraic.  In general the global structure of these solutions is very complicated, despite the fact that locally all branching is finite.  We will show how to determine all equations within particular families for which the solutions are globally finitely branched.  These equations are integrable and can be mapped to equations with the Painlev\'e property.

This talk is part of the Isaac Newton Institute Seminar Series series.

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