Abstract
Poincaré’s geometric theorem claims that an area-preserving diffeomorphism of an annulus which shifts the boundary circles at opposite directions has at least two fixed points. The present paper consists of two parts. In the first one, we show that such a diffeomorphism has more than just two fixed points provided the shift of the boundaries is large enough. In the second part, we prove symplectic fixed point theorems which can be viewed as generalizations of Poincaré’s geometric theorem to higher dimensions.
The work has been partially supported by the ISF grant MSD000 and the INTAS grant 4373.
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© 1997 Birkhäuser Boston
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Chekanov, Y.V. (1997). New generalizations of Poincaré’s geometric theorem. In: Arnold, V.I., Gelfand, I.M., Retakh, V.S., Smirnov, M. (eds) The Arnold-Gelfand Mathematical Seminars. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4122-5_6
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DOI: https://doi.org/10.1007/978-1-4612-4122-5_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8663-9
Online ISBN: 978-1-4612-4122-5
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