Devil’s Staircase – Rotation Number of Outer Billiard with Polygonal Invariant Curves
نویسنده
چکیده
In this paper, we discuss rotation number on the invariant curve of a one parameter family of outer billiard tables. Given a convex polygon η, we can construct an outer billiard table T by cutting out a fixed area A from the interior of η. T is piece-wise hyperbolic and the polygon η is an invariant curve of T under the billiard map φ. We will show that, if β ∈ η is a periodic point under φ with rational rotation number τ = p q , then φ is not the local identity at β. This proves that the rotation number τ as a function of the parameter A is a devil’s staircase function.
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