Topological classification of polynomial complex differential equations with all the critical points of centre type

Abstract

In this paper, we study the global phase portrait of complex polynomial differential equations of degree n of the form , having all their critical points of centre type. We give the exact number of topologically different phase portraits on the Poincaré disk when and in the remaining cases, an upper bound for this number in terms of n.

AMS Subject Classification::

• ordinary differential equation
• phase portrait
• critical point
• centre
• planar graph
• separatrix configuration

AMS Subject Classification::

• 37C10
• 34C05
• 32A10
• 34A34

Notes

1. [email protected]

2. [email protected]

Additional information

Notes on contributors

A. Gasull

1

R. Prohens

2