From Apollonius to Zaremba: Local-global phenomena in thin orbits
From Apollonius to Zaremba: Local-global phenomena in thin orbits
We discuss a number of natural problems in arithmetic, arising in completely unrelated settings, which turn out to have a common formulation involving “thin” orbits. These include the local-global problem for integral Apollonian gaskets and Zaremba’s Conjecture on finite continued fractions with absolutely bounded partial quotients. Though these problems could …