Local Rank of Ergodic Symmetric $n$-Powers does not exceed $n!n^{-n}$

Details Local Rank of Ergodic Symmetric $n$-Powers does not exceed $n!n^{-n}$ Local Rank of Ergodic Symmetric $n$-Powers does not exceed $n!n^{-n}$

2011-08-29

arxiv.org/abs/1108.5660v1

Mathematics

Dynamical Systems

Ergodic theory

Scientific paper

We prove that local rank of an ergodic symmetric power $T^{\odot n}$ does not
exceed $n!n^{-n}$. A. Katok's old results show that this upper bound is exact.
We prove also that $T^{\odot n}$ has infinite Rank as $n>1$.

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