abstract: (joint work with Nataliia Goncharuk)
Given an orientation preserving analytic circle diffeomorphism f:RZ->RZ and a complex number omega in the upper half-plane, we may glue via f the two sides of the subannulus of CZ bounded by RZ and RZ+omega. We obtain a complex torus Eomega isomorphic to C(Z+tau Z) for some tau=tau(omega) in CZ, the class to RZ in Eomega corresponding to the class of RZ in C(Z+tau Z). We study the limit of tau(omega) as the imaginary part of omega tends to 0.