49 citations · 94 across the 21 of their papers we have counts for
21 papers
Measure and integration on Boolean algebras of regular open subsets in a topological space
Marcus Pivato, Vassili Vergopoulos
The regular open subsets of a topological space form a Boolean algebra, where the `join' of two regular open sets is the interior of the closure of their union. A `credence' is a f…
Dynamic and stochastic systems as a framework for metaphysics and the philosophy of science
Christian List, Marcus Pivato
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) th…
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…