Local and global phase portrait of equation $\dot z=f(z)$

Antonio Garijo; Armengol Gasull; Xavier Jarque

doi:10.3934/dcds.2007.17.309

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2007, Volume 17, Issue 2: 309-329. Doi: 10.3934/dcds.2007.17.309

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Local and global phase portrait of equation $\dot z=f(z)$

1.
Dep. d’Eng. Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Pa¨ısos Catalans, 26, 43007 Tarragona
2.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193-Bellaterra
3.
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona

Received: November 30, 2005

Revised: August 31, 2006

Published: April 2007

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Abstract

This paper studies the differential equation $\dot z=f(z)$, where $f$ is an analytic function in $\mathbb C$ except, possibly, at isolated singularities. We give a unify treatment of well known results and provide new insight into the local normal forms and global properties of the solutions for this family of differential equations.

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Mathematics Subject Classification: 34C20, 34A34, 32A10, 37C10.

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