Cubic polynomials: a measurable view on parameter space

Romain Dujardin (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Romain Dujardin. Cubic polynomials: a measurable view on parameter space. Dierk Schleicher. Complex Dynamics, A K Peters. CRC Press, pp.451-489, 2009, 978-1-56881-450-6. ⟨10.1201/b10617-15⟩. ⟨hal-00836320⟩