Embedding odometers in cellular automata (2009)
Coven, Ethan M., Yassawi, Reem
We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be be embedded in a gliders with reflecting walls cellular automaton, which...
A Characterization of the Morse Minimal Set up to Topological Conjugacy (2007)
Coven, Ethan M., Keane, Michael, LeMasurier, Michelle
We establish necessary and sufficient conditions for a dynamical system to be topologically conjugate to the Morse minimal set, the shift orbit closure of the Morse sequence, and conditions for...
On the genesis of symbolic dynamics as we know it (2006)
Coven, Ethan M., Nitecki, Zbigniew H.
WE trace the beginning of symbolic dynamics--the study of the shift dynamical system--as it arose from the use of coding to study recurrence and transitivity properties of geodesics. The normal...
Every compact metric space that supports a positively expansive homeomorphism is finite (2006)
Coven, Ethan M., Keane, Michael
We give a simple proof of the title.
Prevalence of Odometers in Cellular Automata (2005)
Coven, Ethan M., Pivato, Marcus, Yassawi, Reem
We consider a left permutive cellular automaton Phi, with no memory and positive anticipation, defined on the space of all doubly infinite sequences with entries from a finite alphabet. For each such...
The Symbolic Dynamics of Tiling the Integers (1998)
Coven, Ethan M., Geller, William, Silberger, Sylvia, Thurston, William P.
A finite collection $P$ of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of $P$. We associate with such a tiling a doubly infinite...
Tiling the integers with translates of one finite set (1998)
Coven, Ethan M., Meyerowitz, Aaron D.
A set is said to tile the integers if and only if the integers can be written as a disjoint union of translates of that set. We consider the problem of finding necessary and sufficient conditions for...
Tiling the Integers with Translates of One Finite Set (1998)
Ethan M. Coven, Aaron Meyerowitz
. A set tiles the integers if and only if the integers can be written as a disjoint union of translates of that set. We consider the problem of finding necessary and sufficient conditions for a...