3 citations · 6 across the 10 of their papers we have counts for
10 papers
Polynomial maps which are not good for nice recurrence and applications
Rigoberto Zelada
Let be the finite field with two elements and let denote the countably infinite-dimensional vector space over . We show that, unlike the…
Sets of large values of polynomial multi-correlation functions
Vitaly Bergelson, Rigoberto Zelada
Let be non-constant polynomials with zero constant term. The ergodic theoretical proofs of the polynomial and the IP-polynomial Szemeredi theorems a…
Multipliers and Disjointness from Mixing
Sohail Farhangi, Joel Moreira, Rigoberto Zelada
In 2005, Parreau proved that if a measure preserving system is not strongly mixing then it contains a non-trivial factor that is disjoint from every strongly mixing system. Taking…
Weak mixing for area preserving flows on surfaces
Adam Kanigowski, Alexey Okunev, Rigoberto Zelada
Let be an area-preserving smooth flow on a compact, connected, orientable surface with at least one but finitely many fixed points. Assume that is anal…
Coexistence of mixing and rigid behaviors in ergodic theory
Rigoberto Zelada
In this paper we introduce and explore the notion of rigidity group, associated with a collection of finitely many sequences, and show that this concept has many, somewhat surprisi…
A non-mixing Arnold flow on a surface
Bassam Fayad, Adam Kanigowski, Rigoberto Zelada
We construct a smooth area preserving flow on a genus 2 surface with exactly one open uniquely ergodic component, that is asymmetrically bounded by separatrices of non-degenerate s…
Failure of Khintchine-type results along the polynomial image of IP sets
Rigoberto Zelada
In "IP-sets and polynomial recurrence", Bergelson, Furstenberg, and McCutcheon established the following far reaching extension of Khintchine's recurrence theorem: For any invertib…
Mixing and rigidity along asymptotically linearly independent sequences
Rigoberto Zelada
We utilize Gaussian measure preserving systems to prove the existence and genericity of Lebesgue measure preserving transformations which exhibit both mi…
Strongly mixing systems are almost strongly mixing of all orders
Vitaly Bergelson, Rigoberto Zelada
We prove that any strongly mixing action of a countable abelian group on a probability space has higher order mixing properties. This is achieved via introducing and utilizing $\ma…
Iterated differences sets, diophantine approximations and applications
Vitaly Bergelson, Rigoberto Zelada
Let be an odd real polynomial (i.e. a polynomial of the form ). We utilize sets of iterated differences to establish new results about sets of the…