April  2007, 17(2): 309-329. doi: 10.3934/dcds.2007.17.309

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, Spain

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, Spain

Received  December 2005 Revised  September 2006 Published  November 2006

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.
Citation: Antonio Garijo, Armengol Gasull, Xavier Jarque. Local and global phase portrait of equation $\dot z=f(z)$. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 309-329. doi: 10.3934/dcds.2007.17.309
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