Growth of maps, distortion in groups and symplectic geometry |
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Authors: | Leonid Polterovich |
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Institution: | (1) School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel 69978, IL |
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Abstract: | In the present paper we study two sequences of real numbers associated to a symplectic diffeomorphism:?• The uniform norm
of the differential of its n-th iteration;?• The word length of its n-th iteration, where we assume that our diffeomorphism lies in a finitely generated group of symplectic diffeomorphisms.?We
find lower bounds for the growth rates of these sequences in a number of situations. These bounds depend on the symplectic
geometry of the manifold rather than on the specific choice of a diffeomorphism. They are obtained by using recent results
of Schwarz on Floer homology. As an application, we prove non-existence of certain non-linear symplectic representations for
finitely generated groups.
Oblatum 6-XII-2001 & 19-VI-2002?Published online: 5 September 2002
RID="*"
ID="*"Supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. |
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