10 papers
Pointwise ergodic averages along the Omega function in number fields
Diego Céspedes, Sebastián Donoso
We study a general criterion for guaranteeing that an ergodic average exhibits the strong sweeping-out property. This result implies, in particular, the failure of pointwise conver…
Cube structures of the universal minimal system, nilsystems and applications
Axel Ãlvarez, Sebastián Donoso
We propose and develop an approach to study nilsystems and their proximal extensions using cube structures associated with the universal minimal system. We provide alternative proo…
Partition regularity in imaginary quadratic rings of integers
Sebastián Donoso, Andreu Ferré Moragues, Andreas Koutsogiannis +1
We obtain partition regularity results for homogeneous quadratic equations whose parametrized solutions admit nice factorizations into linear forms over rings of integers of imagin…
Ergodic averages for commutative transformations along return times
Sebastián Donoso, Sovanlal Mondal, Vicente Saavedra-Araya
In this paper, we extend recent results on the convergence of ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems, partially a…
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…
A pointwise ergodic theorem along return times of rapidly mixing systems
Sebastián Donoso, Alejandro Maass, Vicente Saavedra-Araya
We introduce a new class of sparse sequences that are ergodic and pointwise universally -good for ergodic averages. That is, sequences along which the ergodic averages converg…