Cubic polynomials: a measurable view on parameter space

Details Cubic polynomials: a measurable view on parameter space Cubic polynomials: a measurable view on parameter space

2006-05-26

arxiv.org/abs/math/0605687v1

Mathematics

Dynamical Systems

Scientific paper

We study the fine geometric structure of bifurcation currents in the parameter space of cubic polynomials viewed as dynamical systems. In particular we prove that these currents have some laminar structure in a large region of parameter space, reflecting the possibility of quasiconformal deformations. On the other hand, there is a natural bifurcation measure, supported on the closure of rigid parameters. We prove a strong non laminarity statement relative to this measure.

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