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Displaying similar documents to “Integrable analytic vector fields with a nilpotent linear part”

Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem

B. Jakubczyk (2000)

Annales Polonici Mathematici

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We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.

A p -adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity

Adrian Jenkins, Steven Spallone (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this note, we consider the question of local analytic equivalence of analytic functions which fix the origin and are tangent to the identity. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered p -adic norms. We show that any two mappings f and g which are formally equivalent are also analytically equivalent. We consider the related questions of roots and centralizers for analytic mappings. In this setting, anything which can...