49 citations · 94 across the 21 of their papers we have counts for
18 papers · 1 filter
Positive expansiveness versus network dimension in symbolic dynamical systems
Marcus Pivato
A `symbolic dynamical system' is a continuous transformation F:X-->X of a closed perfect subset X of A^V, where A is a finite set and V is countable. (Examples include subshifts, o…
Embedding Bratteli-Vershik systems in cellular automata
Marcus Pivato, Reem Yassawi
Many dynamical systems can be naturally represented as `Bratteli-Vershik' (or `adic') systems, which provide an appealing combinatorial description of their dynamics. If an adic sy…
Module Shifts and Measure Rigidity in Linear Cellular Automata
Marcus Pivato
Suppose R is a finite commutative ring of prime characteristic, A is a finite R-module, M:=Z^D x N^E, and F is an R-linear cellular automaton on A^M. If mu is an F-invariant measur…
Attractiveness of the Haar measure for linear cellular automata on Markov subgroups
Alejandro Maass, Servet Mart\'{ı}nez, Marcus Pivato +1
For the action of an algebraic cellular automaton on a Markov subgroup, we show that the Cesàro mean of the iterates of a Markov measure converges to the Haar measure. This is prov…
Prevalence of Odometers in Cellular Automata
Ethan M. Coven, Marcus Pivato, Reem Yassawi +1
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 alph…
Algebraic invariants for crystallographic defects in cellular automata
Marcus Pivato
Let L:= Z^D be the D-dimensional lattice and let A^L be the Cantor space of L-indexed configurations in some finite alphabet A, with the natural L-action by shifts. A `cellular aut…