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Structure of 2-step nilpotent ergodic averages for distinct-degree polynomials
Andreas Koutsogiannis, Borys Kuca, Wenbo Sun
We investigate manifestations of the Nilpotent Heuristic, which posits that recurrence and convergence phenomena known for measure-preserving -systems extend to nilpo…
Resolving the joint ergodicity problem for Hardy sequences
Sebastián Donoso, Andreas Koutsogiannis, Borys Kuca +2
The joint ergodicity classification problem aims to characterize those sequences which are jointly ergodic along an arbitrary dynamical system if and only if they satisfy two natur…
Seminorm estimates and joint ergodicity for pairwise independent Hardy sequences
Sebastián Donoso, Andreas Koutsogiannis, Borys Kuca +2
We develop a robust structure theory for multiple ergodic averages of commuting transformations along Hardy sequences of polynomial growth. We then apply it to derive a number of n…
Joint transitivity for linear iterates
Sebastián Donoso, Andreas Koutsogiannis, Wenbo Sun
We establish sufficient and necessary conditions for the joint transitivity of linear iterates in a minimal topological dynamical system with commuting transformations. This result…
Averages of completely multiplicative functions over the Gaussian integers -- a dynamical approach
Sebastián Donoso, Anh N. Le, Joel Moreira +1
We prove a pointwise convergence result for additive ergodic averages associated with certain multiplicative actions of the Gaussian integers. We derive several applications in dyn…