I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2005, VOLUME 11, NUMBER 5, PAGES 47-55
A bound for the topological entropy of homeomorphisms of
a punctured two-dimensional disk
O. N. Biryukov
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We consider homeomorphisms of a punctured
a finite set of interior points of , which leave
the boundary points fixed.
Any such homeomorphism induces an automorphism of the
fundamental group of .
Moreover, to each homeomorphism , a matrix
can be assigned by using the
well-known Burau representation.
The purpose of this paper is to find a nontrivial lower bound for
the topological entropy of .
First, we consider the lower bound for the entropy found by
R. Bowen by using the growth rate of the induced
Then we analyze the argument of B. Kolev, who obtained
a lower bound for the topological entropy by using the spectral
radius of the matrix , where
, and slightly improve his result.
Last modified: February 26, 2006