Curves of period two points for trace maps

Humphries, Stephen; Manning, Anthony

doi:10.1090/S0002-9947-2014-06367-8

Curves of period two points for trace maps
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by Stephen P. Humphries and Anthony Manning PDF

Trans. Amer. Math. Soc. 367 (2015), 5721-5751 Request permission

Abstract:

We consider an infinite family of trace maps $\alpha _n$ and their action on $\mathbb R^3$. Trace maps fix certain invariant surfaces, and in an earlier paper we found that the fixed points for $\alpha _n$ on one such surface were joined in pairs by curves of fixed points, thus determining a ‘duality’ for such fixed points. We now extend this idea to determine the duality for all the points of period $2$ that lie in the planes $x=\pm y$ and for certain others that do not.

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