Differential and Integral Equations

A Poincaré index formula for surfaces with boundary

Jaume Llibre and Jordi Villadelprat

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We give an easy extension of the Poincaré Index Formula from the disc to any surface with boundary. In particular we show that the sum of the indices of the vector field at the critical points depends only on the Euler characteristic of the surface and on the behaviour of its trajectories in the boundary. Our theorem improves previous results on the same formula.

Article information

Differential Integral Equations, Volume 11, Number 1 (1998), 191-199.

First available in Project Euclid: 1 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R25: Vector fields, frame fields
Secondary: 34C05: Location of integral curves, singular points, limit cycles 55M25: Degree, winding number 58F21


Llibre, Jaume; Villadelprat, Jordi. A Poincaré index formula for surfaces with boundary. Differential Integral Equations 11 (1998), no. 1, 191--199. https://projecteuclid.org/euclid.die/1367414143

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