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The gap distribution of slopes on the golden \(L\). (English) Zbl 1332.37027

Bhattacharya, Siddhartha (ed.) et al., Recent trends in ergodic theory and dynamical systems. International conference in honor of S. G. Dani’s 65th birthday, Vadodara, India, December 26–29, 2012. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-0931-9/pbk; 978-1-4704-2219-6/ebook). Contemporary Mathematics 631, 47-62 (2015).
Summary: We give an explicit formula for the limiting gap distribution of slopes of saddle connections on the golden \(L\), or any translation surface in its \(\mathrm{SL}(2,\mathbb{R})\)-orbit, in particular the double pentagon. This is the first explicit computation of the distribution of gaps for a flat surface that is not a torus cover.
For the entire collection see [Zbl 1309.37003].

MSC:

37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37A25 Ergodicity, mixing, rates of mixing
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
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