8 papers
Medvedev degrees of SFTs on cocompact Fuchsian groups
Sebastián Barbieri, Nicanor Carrasco-Vargas, Paul Toussaint
We prove that for any cocompact Fuchsian group the class of Medvedev degrees attained by subshifts of finite type is the class of degrees. This result relies on the constru…
A geometric obstruction to self-simulation for groups
Sebastián Barbieri, Kanéda Blot, Mathieu Sablik +1
We introduce a new quasi-isometry invariant for finitely generated groups and show that every group with this property admits a subshift which is effectively closed by patterns and…
A remark on inverse limits of effective subshifts
Sebastián Barbieri, Leo Poirier
We show that, for every finitely generated group with decidable word problem and undecidable domino problem, there exists a sequence of effective subshifts whose inverse limit is n…
A general framework for quasi-isometries in symbolic dynamics beyond groups
Sebastián Barbieri, Nicolás Bitar
We introduce an algebraic structure which encodes a collection of countable graphs through a set of states, generators and relations. These structures, which we call blueprints, ca…
The automorphism group of a strongly irreducible subshift on a group
Sebastián Barbieri, Nicanor Carrasco-Vargas, Paola Rivera-Burgos
We study the automorphism group of a non-trivial strongly irreducible subshift on an arbitrary infinite group and generalize classical results of Ry…
Cellular automata, percolation and dynamical dichotomies
Sebastián Barbieri, Felipe García-Ramos, Siamak Taati
We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilm…
Medvedev degrees of subshifts on groups
Sebastián Barbieri, Nicanor Carrasco-Vargas
The Medvedev degree of a subshift is a dynamical invariant of computable origin that can be used to compare the complexity of subshifts that contain only uncomputable configuration…
Effective dynamical systems beyond dimension zero and factors of SFTs
Sebastián Barbieri, Nicanor Carrasco-Vargas, Cristóbal Rojas
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable represe…