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Equicontinuity of maps on a dendrite with finite branch points.
- Source :
- Acta Mathematica Sinica; Aug2017, Vol. 33 Issue 8, p1125-1130, 6p
- Publication Year :
- 2017
-
Abstract
- Let ( T, d) be a dendrite with finite branch points and f be a continuous map from T to T. Denote by ω( x, f) and P( f) the ω-limit set of x under f and the set of periodic points of f, respectively. Write Ω( x, f) = { y| there exist a sequence of points x ∈ T and a sequence of positive integers n < n < ··· such that lim x = x and lim $$f^{n_{k}}$$ ( x ) = y}. In this paper, we show that the following statements are equivalent: (1) f is equicontinuous. (2) ω( x, f) = Ω( x, f) for any x ∈ T. (3) ∩ f ( T) = P( f), and ω( x, f) is a periodic orbit for every x ∈ T and map h: x → ω( x, f) ( x ∈ T) is continuous. (4) Ω( x, f) is a periodic orbit for any x ∈ T. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICAL mappings
CONTINUOUS functions
BRANCHING processes
INTEGERS
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 33
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 123927282
- Full Text :
- https://doi.org/10.1007/s10114-017-6289-x