Geometry

   

Solution of Poincare's Vector Field Problem

Authors: John Atwell Moody

When a meromorphic vector field is given on the projective plane, a complete holomorphic limit cycle, because it is a closed singular submanifold of projective space, is defined by algebraic equations. Also the meromorphic vector field is an algebraic object. Poincare had asked, is there just an algebraic calculation leading from the vector field to the defining equations of the solution, without the mysterious intermediary of the dynamical system. The answer is yes, that there is nothing more mysterious or wonderful that happens when a complete holomorphic limit cycle is formed than could have been defined using algebra.

Comments: 17 Pages. written September 2014

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[v1] 2017-07-01 08:14:34

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