DOI: 10.24193/fpt-ro.2021.1.18

Authors: Alexander Kirillov

Abstract: An extension of the Poincaré-Birkhoff fixed point theorem to noninvariant under area-preserving homeomorphism annuli is considered. Unlike the well-known W.-Y. Ding’s theorem [7], the inner boundary component of an annulus is not assumed to be star-shaped, while the outer boundary component is star-shaped. The existence of at least two fixed points for area preserving homeomorphism satisfying some twist condition is proved.

Key Words and Phrases: 54H25, 37E40, 47H10.

2010 Mathematics Subject Classification: Poincaré-Birkhoff fixed point theorem, noninvariant annulus, non-star-shaped boundary.

Published on-line: February 1st, 2021.

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