The aim of this paper is to investigate the connection between transitivity, density of the set of periodic points and topological entropy for low dimensional continuous maps. The paper deals with this problem in the case of the n-star and the circle among the one-dimensional spaces and in some higher dimensional spaces. Particular attention is paid to triangular maps and to extensions of transitive maps to higher dimensions without increasing topological entropy. ©1999 American Mathematical Society .
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 1 Dec 1999|
- Periodic points
- Topological entropy
- Transitive maps
- Triangular maps