Collet, Pierre2007-08-162007-08-161983https://hdl.handle.net/11299/3661We consider holomorphic perturbations f of f0, f0(z) = z2, which are small in a neighborhood of the unit circle (the Julia set of f0). We show that if the C1 conjugacy invariants of f and f0 are identical, then f and f0 are conjugate on their part of the Julia set which remains near the unit circle.