Fixed point index and decompositions of isolated invariant compacta.

Abstract

The author proves that if f is an orientation reversing homeomorphism of the plane and p is an isolated and stable fixed point of f then the fixed point index of f at p is equal to 1 . In the orientation preserving case this result was obtained by E. N. Dancer and R. Ortega [J. Dynam. Differential Equations 6 (1994), no. 4, 631–637. The proof is based on the prime ends compactifications method and a fixed point result by K. M. Kuperberg [Proc. Amer. Math. Soc. 112 (1991), no. 1, 223–229.