Tree maps having chain movable fixed points
| Autor: | Geng-Rong Zhang, Jie-Hua Mai, Xin-He Liu |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Discrete mathematics
Chain equivalent set Topological entropy Block (permutation group theory) Fixed point Chain movable fixed point Combinatorics Set (abstract data type) Chain reachable set Turbulence Metric space Integer Chain (algebraic topology) Chain recurrent point Tree (set theory) Geometry and Topology Mathematics |
| Zdroj: | Topology and its Applications. (16):2572-2579 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2010.07.029 |
| Popis: | In this paper we discuss some basic properties of chain reachable sets and chain equivalent sets of continuous maps. It is proved that if f : T → T is a tree map which has a chain movable fixed point v, and the chain equivalent set CE ( v , f ) is not contained in the set P ( f ) of periodic points of f, then there exists a positive integer p not greater than the number of points in the set End ( [ CE ( v , f ) ] ) − P v ( f ) such that f p is turbulent, and the topological entropy h ( f ) ⩾ ( log 2 ) / p . This result generalizes the corresponding results given in Block and Coven (1986) [2] , Guo et al. (2003) [6] , Sun and Liu (2003) [10] , Ye (2000) [11] , Zhang and Zeng (2004) [12] . In addition, in this paper we also consider metric spaces which may not be trees but have open subsets U such that the closures U ¯ are trees. Maps of such metric spaces which have chain movable fixed points are discussed. |
| Databáze: | OpenAIRE |
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