5 citations · 13 across the 12 of their papers we have counts for
16 papers
On minimal subshifts of linear word complexity with slope less than 3/2
Darren Creutz, Ronnie Pavlov
We prove that every infinite minimal subshift with word complexity satisfying is measure-theoretically isomorphic to its maximal equicontinuous factor…
Low Complexity Subshifts have Discrete Spectrum
Darren Creutz, Ronnie Pavlov
We prove results about subshifts with linear (word) complexity, meaning that , where for every , is the number of -letter words appear…
Measure-Theoretically Mixing Subshifts of Minimal Word Complexity
Darren Creutz
We resolve a long-standing open question on the relationship between measure-theoretic dynamical complexity and symbolic complexity by establishing the exact word complexity at whi…
Word Complexity of (Measure-Theoretically) Weakly Mixing Rank-One Subshifts
Darren Creutz
We exhibit subshifts admitting weakly mixing (probability) measures, for arbitrary , with word complexity satisfying . For arbitrary $f(…
Measure-Theoretically Mixing Subshifts with Low Complexity
Darren Creutz, Ronnie Pavlov, Shaun Rodock
We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any $f :…
Harmonic Functions on Compactly Generated Groups
Darren Creutz
A compactly generated group is noncompact if and only if it admits a nonconstant harmonic function (for some, equivalently for every, reasonable measure). This generalizes the know…