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math.DS2023
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…
math.DS2023
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…