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The index of lyapunov stable fixed points in two dimensions (1994)

Dancer, E. N. ; Ortega, R.

Springer

Journal of dynamics and differential equations 6 (1994), S. 631-637

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ISSN: 1572-9222

Keywords: stability ; fixed point index ; periodic solutions

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR 2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02218851

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