Entropy of homeomorphisms on unimodal inverse limit spaces
Abstract
We prove that every self-homeomorphism
h:
K
s
→
K
s
on the inverse limit space
K
s
of the tent map
T
s
with slope
s∈(
2
–
√
,2]
has topological entropy $\htop(h) = |R| \log s$, where $R \in \Z$ is such that
h
and
σ
R
are isotopic. Conclusions on the possible values of the entropy of homeomorphisms of the inverse limit space of a (renormalizable) quadratic map are drawn as well.