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Analytic obstructions to isochronicity in codimension 1*

Published online by Cambridge University Press:  17 July 2013

Waldo Arriagada-Silva
Waldo Arriagada-Silva*
Affiliation:
Centro de Docencia Superior en Ciencias Básicas, Universidad Austral de Chile, Sede Puero Montt, Chile (waldo.arriagada@uach.cl)
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Abstract

In this paper we study the analytical obstructions preventing the germ of a generic analytic family of elliptic ordinary differential equations from being isochronous. The formal obstructions are purely arithmetical and can be set in terms of commutators. The analytical obstructions arise out of the non-convergence of the normalizing coordinates in the Poincaré–Dulac normalization process. The temporal part of the invariant is the obstruction to isochronicity in a particular context.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 4 , August 2013 , pp. 669 - 688
Copyright
Copyright © Royal Society of Edinburgh 2013 

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