Related papers: On flow-equivalence of R-graph shifts

We will study a certain synchronizing property of subshifts called $\lambda$-synchronization. The $\lambda$-synchronizing subshifts form a large class of irreducible subshifts containing irreducible sofic shifts. We prove that the…

Subshifts with property $(A)$ are constructed from a class of directed graphs. As special cases the Markov-Dyck shifts are shown to have property $(A)$. The semigroups, that are associated to $\mathcal R$-graph shifts with Property (A), are…

We prove that the Karoubi envelope of a shift --- defined as the Karoubi envelope of the syntactic semigroup of the language of blocks of the shift --- is, up to natural equivalence of categories, an invariant of flow equivalence. More…

We study two problems related to flow equivalence of shift spaces. The first problem, the classification of $S$-gap shifts up to flow equivalence, is partially solved with the establishment of a new invariant for the sofic $S$-gap shifts…

We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients: (1) An extension theorem, for extending…

We study basic properties of flow equivalence on one-dimensional compact metric spaces with a particular emphasis on isotopy in the group of (self-) flow equivalences on such a space. In particular, we show that an orbit-preserving such map…

The flow semigroup, introduced by John Rhodes, is an invariant for digraphs and a complete invariant for graphs. After collecting together previous partial results, we refine and prove Rhodes's conjecture on the structure of the maximal…

We define $G$-cospectrality of two $G$-gain graphs $(\Gamma,\psi)$ and $(\Gamma',\psi')$, proving that it is a switching isomorphism invariant. When $G$ is a finite group, we prove that $G$-cospectrality is equivalent to cospectrality with…

To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of…

In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we classify finite semigroups such that the…

A certain synchronizing property for subshifts called $\lambda$-synchronization yields $\lambda$-graph systems called the $\lambda$-synchronizing $\lambda$-graph systems for the subshifts. The $\lambda$-synchronizing $\lambda$-graph system…

We analyze in the context of Leavitt path algebras some graph operations introduced in the context of symbolic dynamics by Williams, Parry and Sullivan, and Franks. We show that these operations induce Morita equivalence of the…

Shifts of finite type defined from shift equivalent matrices must be flow equivalent.

Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for…

In this paper, a G-shift of finite type (G-SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G. We reduce the classification of G-SFTs up to equivariant flow equivalence to an algebraic…

We consider impulsive semiflows and establish sufficient conditions to the existence of invariant measures. Namely, the impulsive set and its image are both submanifolds of codimension one that are transversal to the flow direction.…

To every half-translation surface, we associate a saddle connection graph, which is a subgraph of the arc graph. We prove that every isomorphism between two saddle connection graphs is induced by an affine homeomorphism between the…

Let $\Gamma$ be a multigraph with for each vertex a cyclic order of the edges incident with it. For $n \geq 3$, let $D_{2n}$ be the dihedral group of order $2n$. Define $\mathbb{D} := \{(\begin{smallmatrix} 1 & a \\ 0 & 1 \end{smallmatrix})…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

Combining the the results of A.R. Meyer and L.J. Stockmeyer "The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space", and K.S. Booth "Isomorphism testing for graphs, semigroups, and finite automata are…