7 papers
An affirmative answer to Owings's sumset question
Wen Huang, Zhengxing Lian, Song Shao +3
We give an affirmative answer to Owings's sumset question: for any -coloring of natural numbers, there is an infinite such that is monochromatic. Mo…
Maximal pronilfactors and a topological Wiener-Wintner theorem
Yonatan Gutman, Zhengxing Lian
For strictly ergodic systems, we introduce the class of CF-Nil() systems: systems for which the maximal measurable and maximal topological -step pronilfactors coincide as mea…
Pro-nilfactors of the space of arithmetic progressions in topological dynamical systems
Zhengxing Lian, Jiahao Qiu
For a topological dynamical system , and , let and be the orbit closures of the diagonal point ( times) un…
Minimal systems with finitely many ergodic measures
Wen Huang, Zhengxing Lian, Song Shao +1
In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measur…
A counter-example for polynomial version of Sarnak's conjecture
Zhengxing Lian, Ruxi Shi
We construct the counter-example for polynomial version of Sarnak's conjecture for minimal systems, which assets that the Möbius function is linearly disjoint from subsequences alo…
Strictly ergodic distal models and a new approach to the Host-Kra factors
Yonatan Gutman, Zhengxing Lian
Cocycles are a key object in Antolín Camarena and Szegedy's (topological) theory of nilspaces. We introduce measurable counterparts, named nilcycles, enabling us to give conditions…