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Pré-Publication, Document De Travail Année : 2018

Solution to Briot and Bouquet problem on singularities of differential equations

Résumé

We solve Briot and Bouquet problem (1856) on the existence of non-monodromic (multivalued) solutions for singularities of differential equations in the complex domain. The solution is an application of hedgehog dynamics for indifferent irrational fixed points. We present an important simplification by only using a local hedgehog for which we give a simpler and direct construction of quasi-invariant curves which does not rely on complex renormalization.
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Dates et versions

hal-01707628 , version 1 (12-02-2018)
hal-01707628 , version 2 (16-02-2018)
hal-01707628 , version 3 (06-03-2018)

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  • HAL Id : hal-01707628 , version 1

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Ricardo Pérez-Marco. Solution to Briot and Bouquet problem on singularities of differential equations. 2018. ⟨hal-01707628v1⟩
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