We show that if two piecewise C2 Generalized Interval Exchange Transformations f and g of generic rotation number with mean-nonlinearity 0 are homeomorphic, boundary equivalent and their renormalizations approach affine interval exchange transformations, then their respective renormalizations converge to each other and the conjugating map is C1. Moreover, if f and g are GIETs with rotation type combinatorial data, generic rotation number and they are break-equivalent as piecewise circle diffeomorphisms, they are actually C1-conjugated as circle diffeomorphisms. This is a joint work with Frank Trujillo.
Meeting ID: 852 4277 3200 Passcode: 103121