HOROWITZ SEMINAR
PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS
Monday, 28/12/2009, at 14:30 in: room 210, Schreiber Bldg.
Michael Hochman (Princeton)
will speak on
Non-expansive directions of Z2 actions
ABSTRACT:
A line L in the plane is expansive for a symbolic Z2 subshift if, for some r>0,
any two configurations which agree on an r-neighborhood of L must agree everywhere.
In a paper from 1995 Lind and Boyle studied the set of non-expansive directions of an action,
showing that it is closed and, for infinite subshifts, non-empty.
They also showed that any closed set of directions containing at least 2 points occurs in this way (this was proved for general Z2 actions).
The question of whether a system can have a single non-expansive direction (in a non-trivial way) has remained open for some time.
This question is related to the existence of cellular automata which act without equicontinuity points, but with sub-linear rate of "information propagation".
I will discuss the recent resolution of these questions.
To suggest a talk (yours, or someone elses), contact
Jon. Aaronson:
aaro at post dot tau dot ac dot il