6 papers
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 RodrÃguez-MartÃn, 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…