Global behavior of solutions of nonlinear ODEs in $\CC$: first order equations

Mathematics – Classical Analysis and ODEs

Scientific paper

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Scientific paper

We show that the solutions of first order nonlinear ODEs can be controlled
globally in the complex domain, using a finite set of constants of motion
defined in regions of $\CC$. These constants of motion enable us to obtain
quantitative behaviors of the solutions far away from the origin, as well as to
determine the position of singularities of the solution.

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