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On self-similarities of ergodic flows | | Alexandre I. Danilenko
; Valery V. Ryzhikov
; | | Date: |
1 Nov 2010 | | Abstract: | Given an ergodic flow $T=(T_t)_{tinBbb R}$, let $I(T)$ be the set of reals
$s
e 0$ for which the flows $(T_{st})_{tinBbb R}$ and $T$ are isomorphic. It
is proved that $I(T)$ is a Borel subset of $Bbb R^*$. It carries a natural
Polish group topology which is stronger than the topology induced from $Bbb
R$. There exists a mixing flow $T$ such that $I(T)$ is an uncountable meager
subset of $Bbb R^*$.
For a generic flow $T$, the transformations $T_{t_1}$ and $T_{t_2}$ are
spectrally disjoint whenever $|t_1|
e |t_2|$.
A generic transformation (i) embeds into a flow $T$ with $I(T)={1}$ and
(ii) does not embed into a flow with $I(T)
e {1}$. For each countable
multiplicative subgroup $SsubsetBbb R_+^*$, it is constructed a Poisson (and
Gaussian) flow $T$ with simple spectrum such that $I(T)capBbb R^*_+=S$. If
$S$ is without rational relations then there is a rank-one weakly mixing rigid
flow $T$ with $I(T)=S$. | | Source: | arXiv, 1011.0343 | | Services: | Forum | Review | PDF | Favorites | |
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