Earthquakes and Thurston's boundary for the Teichmuller space of the universal hyperbolic solenoid

A measured lamination on the universal hyperbolic solenoid S is, by our definition, a leafwise measured lamination with appropriate continuity for the transverse variations. An earthquakes on the universal hyperbolic solenoid S is uniquely determined by a measured lamination on S; it is a leafwise earthquake with the leafwise earthquake measure equal to the leafwise measured lamination. Leafwise earthquakes fit together to produce a new hyperbolic metric on S which is transversely continuous, and we show that any two hyperbolic metrics on S are connected by an earthquake. We also establish the space of projective measured lamination PML(S) as a natural Thurston-type boundary to the Teichmuller space T(S) of the universal hyperbolic solenoid S. The baseleaf-preserving mapping class group MCG(BLP)(S) acts continuously on the closure T(S) boolean OR PML(S) of T(S). Moreover, the set of transversely locally constant measured laminations on S is dense in ML(S).