# Dynamics on the Riemann Sphere

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#### DOI: 10.4171/011-1/7

Semiconjugacies between the Julia sets of geometrically finite rational maps II

Tomoki Kawahira[1]

(1) Nagoya University, Nagoya, Japan

For a geometrically finite rational map f, there exists a perturbation into another geometrically finite rational map which preserves the dynamics on the Julia set nicely. Indeed, we can perturb parabolic cycles of f into attracting cycles and repelling cycles in any combination.