8 papers
A Lipschitz refinement of the Bebutov-Kakutani dynamical embedding theorem for connected Lie group actions
Yonatan Gutman, Qiang Huo, Kangbo Ouyang
Let be a connected Lie group equipped with a compatible right-invariant metric and let act continuously on a compact metrizable space . We prove that admits a -eq…
Odd order cases of Chowla's averages over arbitrary rectangles
Qiang Huo, Zhengxing Lian, Kangbo Ouyang
Let be the Liouville function. In this paper we prove an average form of Chowla Conjecture for even . that is, for every fixed even integer , we prove that \[ \lim…
Connectedness of polynomial diagonal orbit closures for minimal nilrotations and applications
Kangbo Ouyang, Jiahao Qiu, Xiangdong Ye
For a minimal nilrotation on a compact connected nilmanifold, we prove that the polynomial diagonal orbit closure associated with any finite family of polynomials with integer coef…
Maximal pattern complexity and structure of null systems
Jie Li, Kangbo Ouyang
A compact metrizable system is null if its topological sequence entropy vanishes along every sequence of times. We prove that nullness is equivalent to polynomial maximal pattern c…
Zero-Threshold Discrepancies for Multiple Correlation Sequences
Kangbo Ouyang, Jiahao Qiu, Xiangdong Ye
We study the zero-threshold lifting problem for polynomial multiple correlation sequences with respect to the measure-theoretic pro-nilfactor. The structure theory for polynomial m…
Bohr obstructions to recurrence along Hardy-field sequences
Kangbo Ouyang, Saúl Rodríguez-Martín, Leiye Xu +1
We construct Bohr obstructions to multiple recurrence along rounded Hardy-field sequences, showing that the real derivative-span criterion of Bergelson, Moreira, and Richter is ess…
Fractal transference principles for subsets of of positive density
Zhuowen Guo, Kangbo Ouyang, Jiahao Qiu +1
We establish a multidimensional fractal transference principle for digit-restricted sets associated with subsets of , extending the one-dimensional framework of Nakaj…
CF-Nil systems and convergence of two-dimensional ergodic averages
Kangbo Ouyang, Qinqi Wu
A topological dynamical system is called CF-Nil() if it is strictly ergodic and the maximal measurable and maximal topological -step pro-nilfactors coincide as measur…