Highly Influenced

# Periods Implying Almost All Periods, Trees with Snowflakes and Zero Entropy Maps

@inproceedings{Blokh1990PeriodsIA, title={Periods Implying Almost All Periods, Trees with Snowflakes and Zero Entropy Maps}, author={A M Blokh}, year={1990} }

- Published 1990

Let X be a compact tree and f : X − → X be a continuous map; denote by End(X) the number of endpoints of X and by Edg(X) the number of edges of X. In Section 2 we prove the following statements: (1) if n > 1 is an integer with no prime divisors less than End(X) + 1 and f has a cycle of period n, then f has cycles of all periods greater than 2End(X)(n − 1), and if h(f) is its topological entropy then h(f) ≥ ln 2 nEnd(X) − 1 ; (2) if 0 < n < End(X) + 1 and E is the set of all periods of cycles of… CONTINUE READING