On the set of periods of sigma-maps of degree 1
Discrete Contin. Dyn. Syst. Ser. A, 35, No. 10, 4683-4734, 2015.
We study the set of periods of degree 1 continuous maps from sigma
into itself, where sigma denotes the space shaped like the letter
(i.e., a segment attached to a circle by one of its endpoints). Since the
maps under consideration have degree 1, the rotation theory can be used.
We show that, when the interior of the rotation interval contains an integer,
then the set of periods (of periodic points of any rotation number) is the
set of all integers except maybe 1 or 2. We exhibit degree 1 sgma-maps f
whose set of periods is a combination of the set of periods of a degree 1
circle map and the set of periods of a 3-star (that is, a space shaped like
the letter Y). Moreover, we study the set of periods forced by periodic
orbits that do not intersect the circuit of sigma; in particular,
when there exists such a periodic orbit whose diameter (in the covering space)
is at least 1, then there exist periodic points of all periods.
[pdf (published paper)]