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Alpern Lemma Independent of a Partition for Aperiodic Systems
Nishant Chandgotia, Zemer Kosloff, Shrey Sanadhya
We prove that for every , an aperiodic, probability preserving system and a finite measurable partition of , there exists an Alpern Multitower…
Trace spectra of simplices in large sets
Michael Björklund, Alexander Fish, Shrey Sanadhya
Given an ordered tuple of vectors in , let be its edge matrix. We prove that, in every fin…
Subdiagrams and invariant measures for generalized Bratteli diagrams
Sergey Bezuglyi, Palle Jorgensen, Olena Karpel +2
The results of this paper contribute to the study of invariant measures of Borel dynamical systems that can be modeled using generalized Bratteli diagrams. In this context, we stud…
Counterexamples to double recurrence for non-commuting deterministic transformations
Zemer Kosloff, Shrey Sanadhya
We show that if are injective, integer polynomials that vanish at the origin, such that either both are of degree or both are of degree or higher, then double rec…
Multidimensional local limit theorem in deterministic systems and an application to non-convergence of polynomial multiple averages
Zemer Kosloff, Shrey Sanadhya
We show that for every ergodic and aperiodic probability preserving system , there exists , whose corresponding cocycle satisfies the -…
Periodicity of joint co-tiles in
Tom Meyerovitch, Shrey Sanadhya, Yaar Solomon
An old theorem of Newman asserts that any tiling of by a finite set is periodic. A few years ago, Bhattacharya proved the periodic tiling conjecture in .…
Bratteli diagrams in Borel dynamics
Sergey Bezuglyi, Palle E. T. Jorgensen, Olena Karpel +1
Bratteli-Vershik models have been very successfully applied to the study of various dynamical systems, in particular, in Cantor dynamics. In this paper, we study dynamics on the pa…
Substitution-dynamics and invariant measures for infinite alphabet-path space
Sergey Bezuglyi, Palle E. T. Jorgensen, Shrey Sanadhya
We study substitutions on countably infinite alphabet (without compactification) as Borel dynamical systems. We construct stationary and non-stationary generalized Bratteli-Vershik…
A shrinking target theorem for ergodic transformations of the unit interval
Shrey Sanadhya
We show that for any ergodic Lebesgue measure preserving transformation and any decreasing sequence of positive real numbers w…
Coboundaries of commuting Borel automorphisms
Shrey Sanadhya
We show that if are two commuting automorphisms of standard Borel space such that they generate a free Borel -action then and do not have same sets of real valu…
Cohomology of hyperfinite Borel actions
Sergey Bezuglyi, Shrey Sanadhya
We study cocycles of countable groups of Borel automorphisms of a standard Borel space taking values in a locally compact second countable group . We prov…