Topological rigidity of unfoldings of resonant diffeomorphisms

5007-37-511
Javier Ribón* ([email protected]), Rua Mário Santos Braga, S/N, Campus do Valonguinho,
Centro, Niterói, 24020-140, Brazil. Topological rigidity of unfoldings of resonant diffeomorphisms.
We prove that a homeomorphism conjugating two generic 1-parameter unfoldings of 1-variable complex analytic resonant
diffeomorphisms is holomorphic or anti-holomorphic by restriction to the unperturbed parameter. We provide examples
that show that the genericity hypothesis is necessary. Moreover we characterize the possible behavior of conjugacies for
the unperturbed parameter in the general case. In particular they are always real analytic outside of the origin.
We describe the structure of the limits of orbits when we approach the unperturbed parameter. The proof of the
rigidity results is based on the study of the action of a topological conjugation on the limits of orbits. (Received May 14,
2013)
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