Differential and Integral Equations

A Poincaré index formula for surfaces with boundary

Jaume Llibre and Jordi Villadelprat

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Abstract

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

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

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367414143

Mathematical Reviews number (MathSciNet)
MR1607604

Zentralblatt MATH identifier
1004.57024

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

Citation

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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