Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved th...Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.展开更多
This is a study of one dimensional generalized birth-death chains in a random environment (GBDIRE). We give two sufficient conditions of recurrence for GBDIRE.
Let X be a metric space. We say that a continuous surjection f:X→X is a topological Anosov map (abbrev. TA map) if f is expansive and has pseudo orbit tracing property with respect to some compatible me...Let X be a metric space. We say that a continuous surjection f:X→X is a topological Anosov map (abbrev. TA map) if f is expansive and has pseudo orbit tracing property with respect to some compatible metric for X . This paper studies the properties of TA maps of non compact metric spaces and gives some conditions for the map to be topologically mixing.展开更多
In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a conse...In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a consequence, every star flow on the 2-sphere or the projective plane is singular hyperbolic.展开更多
We introduce the concept of asymptotic pseudo orbit tracing property (APOTP) and obtain a new condition by the APOTP for which a homeomor-phism is a non-wandering homeomorphism.
基金the National Natural Science Foundation of China(1 996 1 0 0 1 ) and SF of Guangxi(0 1 3 5 0 2 7)
文摘Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.
文摘This is a study of one dimensional generalized birth-death chains in a random environment (GBDIRE). We give two sufficient conditions of recurrence for GBDIRE.
文摘Let X be a metric space. We say that a continuous surjection f:X→X is a topological Anosov map (abbrev. TA map) if f is expansive and has pseudo orbit tracing property with respect to some compatible metric for X . This paper studies the properties of TA maps of non compact metric spaces and gives some conditions for the map to be topologically mixing.
基金Supported by National Natural Science Foundation of China(Grant No.11201023)Specialized Research Fund for the Doctoral Program of Higher Education
文摘In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a consequence, every star flow on the 2-sphere or the projective plane is singular hyperbolic.
基金Project supported by the National Natural Science Foundation of China(10361001)the Natural Science Foundation of the Committee of Education of Jiangshu Province (02KJB110008).
文摘We introduce the concept of asymptotic pseudo orbit tracing property (APOTP) and obtain a new condition by the APOTP for which a homeomor-phism is a non-wandering homeomorphism.
