Flow equivalence of G-SFTs
Copyright policy )Flow equivalence of G-SFTs
In this paper, a G G -shift of finite type ( G G -SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G G . We reduce the classification of G G -SFTs up to equivariant flow equivalence to an algebraic classification of a class of poset-blocked matrices over the integral group ring of G G . For a special case of two irreducible components with G = Z 2 G=\mathbb {Z}_2 , we compute explicit complete invariants. We relate our matrix structures to the Adler-Kitchens-Marcus group actions approach. We give examples of G G -SFT applications, including a new connection to involutions of cellular automata.
- University of Copenhagen Denmark
- University of Copenhagen Denmark
- University of Maryland, College Park United States
- University of Copenhagen Denmark
- University of the Faroe Islands Faroe Islands
Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems, shift of finite type, Symbolic dynamics, poset-blocked matrices, Dynamical Systems (math.DS), Dynamical systems involving maps of trees and graphs, FOS: Mathematics, Entropy and other invariants, isomorphism, classification in ergodic theory, Mathematics - Dynamical Systems, equivariant dynamical systems, Multidimensional shifts of finite type, Dynamics in general topological spaces
Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems, shift of finite type, Symbolic dynamics, poset-blocked matrices, Dynamical Systems (math.DS), Dynamical systems involving maps of trees and graphs, FOS: Mathematics, Entropy and other invariants, isomorphism, classification in ergodic theory, Mathematics - Dynamical Systems, equivariant dynamical systems, Multidimensional shifts of finite type, Dynamics in general topological spaces
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