Posted in

Speaker:

Dominik Kwietniak
Affiliation:

Jagiellonian U\MPI
Date:

Fri, 2014-06-20 15:30 - 16:30
Location:

MPIM Lecture Hall
Parent event:

Dynamics and Numbers 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.

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