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

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