We 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.
Institute for Mathematics and Its Applications>IMA Preprints Series
Local Cinfinity Conjugacy on the Julia Set for some Holomorphic Perturbations of z to z2.
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