连续自映射拓扑压的两个注记

令T:X→ X是紧度量空间(X,d)上的连续映射.该文给出了T的拓扑压和T在非游荡集上的限制的拓扑压相等的不依赖于变分原理的一个直接证明.同时,还讨论了半共轭的两个系统的拓扑压之间的关系,证明了拓扑压在一致有限对一条件下是半共轭不变量.     

拓扑半共轭关系是个预序但不是偏序

本短文指出，存在着紧致连通空间Y及同胚f：Y→Y，g：Y→Y使得f拓扑半共轭于g，g也拓扑半共轭于f，但f与g不拓扑共轭．据此说明了拓扑半共轭关系是个预序但不是偏序。     

Distributional chaos and factors

We show the existence of a dynamical system without any distributionally scrambled pair which is semiconjugated to a distributionally chaotic factor.     

Topological Semi-Conjugacies Between Adding Machines

Let K = (k ₁, k ₂, . . .) be a sequence of positive integers, and be a topological group with a metric and an additive operation given. The adding machine f _K is the addition-by-one map on Σ _K . Buescu and Stewart (Ergodic Theory Dynam Syst 15:271–290, 1995), Block and Keesling (Topology Appl 140:151–161, 2004) and Banks (Ergodic Theory Dynam Syst 17:505–529, 1997) obtained several equivalent conditions for which two adding machines are topologically conjugate, respectively. In this paper, we have a further discussion about semi-conjugate relationship between adding machines, and give some necessary and sufficient conditions for an adding machine to be semi-conjugate to another one. Moveover, we also prove that a transitive translation on a compact subgroup of Σ _K is isometrically conjugate to an adding machine. Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday     

Persistence of Semi-Trajectories

We consider diffeomorphisms f of a smooth compact riemannian mainfold M and its suspension flow . Assuming some regularity of the stable (unstable) sets at the points we prove the persistence in the future of {f ⁿ (x), n ≥ 0} or , i.e., that C ⁰ small perturbations g of f have a semi-trajectory that closely shadows {f ⁿ (x), n ≥ 0} and that the suspension of g has also a semi-trajectory that closely shadows . In case x belongs to a minimal set of f we show that the assumptions concerning the regularity of stable and unstable sets could be reduced to a neighbourhood of x.