A growth gap for diffeomorphisms of the interval |
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Authors: | Leonid Polterovich Mikhail Sodin |
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Institution: | (1) School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel |
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Abstract: | Given an orientation-preserving diffeomorphism of the interval 0;1], consider the uniform norm of the differential of itsn-th iteration. We get a function ofn called the growth sequence. Its asymptotic behaviour is an interesting invariant, which naturally appears both in geometry
of the diffeomorphism groups and in smooth dynamics. Our main result is the following Gap Theorem: the growth rate of this
sequence is either exponential or at most quadratic withn. Further, we construct diffeomorphisms whose growth sequence has quite irregular behaviour. This construction easily extends
to arbitrary manifolds. |
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Keywords: | |
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