Twist maps, coverings and Brouwer’s translation theorem

Abstract:

We apply the Brouwer Translation Theorem to a class of twist maps of the annulus (which contains ${C^1}$ area preserving maps) to show that, if $h$ belongs to this class, then a certain set ${\mathcal {P}_0}$ of periodic points of $h$ cannot be dense. The definition of ${\mathcal {P}_0}$ does not impose any a priori restrictions on the periods of the points of ${\mathcal {P}_0}$.