Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action o...Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action of a group G,then G contains a free subsemigroup and the action has positive geometric entropy.As a corollary,X admits no sensitive nilpotent group action.展开更多
It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z^d action on X, which answers the two questions raised by us before, ...It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z^d action on X, which answers the two questions raised by us before, In 1979, Mané proved that there is no expansive homeomorphism on infinite dimensional spaces. Contrary to this result, we construct an expansive Z^2 action on an infinite dimensional space. We also construct an expansive Z^2 action on a zero dimensional space but no element in Z^2 is expansive.展开更多
Let X be a Peano continuum having a free arc. If X admits a sensitive open map, then X either is homeomorphic to the closed interval [0, 1], or is homeomorphic to the unit circle S^1.
基金Supported by NSFC(Grant Nos.11771318 and 11790274)。
文摘Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action of a group G,then G contains a free subsemigroup and the action has positive geometric entropy.As a corollary,X admits no sensitive nilpotent group action.
文摘It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z^d action on X, which answers the two questions raised by us before, In 1979, Mané proved that there is no expansive homeomorphism on infinite dimensional spaces. Contrary to this result, we construct an expansive Z^2 action on an infinite dimensional space. We also construct an expansive Z^2 action on a zero dimensional space but no element in Z^2 is expansive.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10801103, 10801126 and 10871142)Natural Sciences Fund for Colleges and Universities in Jiangsu Province (Grant No. 08KJB110010)
文摘In this paper, using the integral method observed by Mai Jiehua recently, we show that no dendrite admits a sensitive commutative group action.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271278 and 11401263)
文摘Let X be a Peano continuum having a free arc. If X admits a sensitive open map, then X either is homeomorphic to the closed interval [0, 1], or is homeomorphic to the unit circle S^1.
