13 citations · 45 across the 19 of their papers we have counts for
18 papers · 1 filter
Invariant random compacts
Bryna Kra, Scott Schmieding
For a compact metric space with a group acting on it continuously, an invariant random compact is a Borel probability measure on the space of nonempty compact subsets of $X…
Finitary Ryan's and local entropy for subshifts
Ville Salo, Scott Schmieding
For the action of a group by homeomorphisms on a space , the automorphism group consists of all self-homeomorphisms of which commute with $x \mapsto…
Isogenies of minimal Cantor systems: from Sturmian to Denjoy and interval exchanges
Scott Schmieding, Christopher-Lloyd Simon
This work is motivated by the study of continued fraction expansions of real numbers: we describe in dynamical terms their orbits under the action of .…
Hyperspatiality for isomorphisms of stabilized automorphism groups of shifts of finite type
Jeremias Epperlein, Scott Schmieding
Given a homeomorphism of a compact metric space , the stabilized automorphism group of the system is the group of self-home…
Chaotic almost minimal actions
Van Cyr, Bryna Kra, Scott Schmieding
Motivated by Furstenberg's Theorem on sets in the circle invariant under multiplication by a non-lacunary semigroup, we define a general class of dynamical systems possessing simil…
On the structure of generic subshifts
Ronnie Pavlov, Scott Schmieding
We investigate generic properties (i.e. properties corresponding to residual sets) in the space of subshifts with the Hausdorff metric. Our results deal with four spaces: the space…
Local finiteness and automorphism groups of low complexity subshifts
Ronnie Pavlov, Scott Schmieding
We prove that for any transitive subshift with word complexity function , if , then the quotient group $\textrm{Au…
Local entropy and stabilized automorphism groups of subshifts
Scott Schmieding
For a homeomorphism of a compact metric space , the stabilized automorphism group consists of all self-homeomorphisms of which…
Symbolic dynamics and the stable algebra of matrices
Mike Boyle, Scott Schmieding
We give an introduction to the "stable algebra of matrices" as related to certain problems in symbolic dynamics. We consider this stable algebra (especially, shift equivalence and…
The stabilized automorphism group of a subshift
Yair Hartman, Bryna Kra, Scott Schmieding
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic…
Random Substitution Tilings and Deviation Phenomena
Scott Schmieding, Rodrigo Treviño
Suppose a set of prototiles allows different substitution rules. In this paper we study tilings of constructed from random application of the substitution rules.…
The Mapping Class Group of a Minimal Subshift
Scott Schmieding, Kitty Yang
For a homeomorphism of a Cantor set , the mapping class group is the group of isotopy classes of orientation-preserving self-homeomorphisms o…
Automorphisms of the shift: Lyapunov exponents, entropy, and the dimension representation
Scott Schmieding
Let be a shift of finite type and its corresponding automorphism group. Associated to are certain Lyapunov exponents $α…
Traces of random operators associated with self-affine Delone sets and Shubin's formula
Scott Schmieding, Rodrigo Treviño
We study operators defined on a Hilbert space defined by a self-affine Delone set and show that the usual trace of a restriction of the operator to finite-dimensional subspaces…
Tiling Spaces have aspherical shape
Scott Schmieding
Going beyond the cohomological invariants attached to tiling spaces via inverse limit constructions, Clark and Hunton introduced shape group invariants, and showed these invariants…
Self affine Delone sets and deviation phenomena
Scott Schmieding, Rodrigo Treviño
We study the growth of norms of ergodic integrals for the translation action on spaces coming from expansive, self-affine Delone sets. The linear map giving the self-affinity induc…
Finite group extensions of shifts of finite type: K-theory, Parry and Livšic
Mike Boyle, Scott Schmieding
This paper extends and applies algebraic invariants and constructions for mixing finite group extensions of shifts of finite type. For a finite abelian group G, Parry showed how to…
Maximal equicontinuous factors and cohomology for tiling spaces
Marcy Barge, Johannes Kellendonk, Scott Schmieding
We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that this map is injective in degree one and has torsion fre…