We introduce a new family of shift spaces - the subordinate
shifts. Using them we prove in an elementary way that for every
nonnegative real number t one can find a shift space with entropy t.
Moreover, we show that there is a connection between positive entropy
and combinatorial independence of a shift space. Positive entropy can
be characterized through existence of a large (in terms of asymptotic
and Shnirelman densities) set of coordinates along which the highest
possible degree of randomness in points from the shift is observed. .
It turns out that the shift space known as "square-free flow" and its
relatives that have been recently extensively studied are all examples
of a subordinate shifts.
Attachment | Size |
---|---|
![]() | 176.28 KB |
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5079
[4] http://www.mpim-bonn.mpg.de/webfm_send/270/1
[5] http://www.mpim-bonn.mpg.de/webfm_send/270