We focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle.We construct a weak mixing minimal special flow with bounded topological c...We focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle.We construct a weak mixing minimal special flow with bounded topological complexity.We also prove that if the roof function is C^(∞),then the special flow has sub-polynomial topological complexity and the time one map meets the condition of Sarnak’s conjecture.展开更多
In this paper,we consider weak horseshoe with bounded-gap-hitting times.For a flow(M,Ф),it is shown that if the time one map(M,Ф_(1))has weak horseshoe with boundedgap-hitting times,so is(M,Ф_(τ))for all τ≠0.In ...In this paper,we consider weak horseshoe with bounded-gap-hitting times.For a flow(M,Ф),it is shown that if the time one map(M,Ф_(1))has weak horseshoe with boundedgap-hitting times,so is(M,Ф_(τ))for all τ≠0.In addition,we prove that for an affine homeomorphism of a compact metric abelian group,positive topological entropy is equivalent to weak horseshoe with bounded-gap-hitting times.展开更多
基金supported by NNSF of China(11431012,11731003)supported by NNSF of China(11801538,11871188).
文摘We focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle.We construct a weak mixing minimal special flow with bounded topological complexity.We also prove that if the roof function is C^(∞),then the special flow has sub-polynomial topological complexity and the time one map meets the condition of Sarnak’s conjecture.
基金Leiye Xu is partially supported by NNSF of China(11801538,11871188)the USTC Research Funds of the Double First-Class Initiative.Junren Zheng is partially supported by NNSF of China(11971455).
文摘In this paper,we consider weak horseshoe with bounded-gap-hitting times.For a flow(M,Ф),it is shown that if the time one map(M,Ф_(1))has weak horseshoe with boundedgap-hitting times,so is(M,Ф_(τ))for all τ≠0.In addition,we prove that for an affine homeomorphism of a compact metric abelian group,positive topological entropy is equivalent to weak horseshoe with bounded-gap-hitting times.
