ODEs with Regular Singular Points

Often multivalued functions appear as solutions to ODEs with so-called regular singular points. Since we're working in the complex plane now, weird things can happen when stitching together local solutions à la Picard--Lindelöf.

Another source for multivalued functions are solutions to parametric algebraic equations: z \mapsto the solution to x^2 - z = 0 is for example the square root "multifunction". Or z \mapsto the solution to x^5 + x + z = 0 is the Bring radical.