Disconnected Julia sets of quartic polynomials and a new topology of the symbol space. (English) Zbl 1154.37018

Summary: For a certain quartic polynomial, there exists a homeomorphism between the set of all components of the filled-in Julia set with the Hausdorff metric and some subset of the corresponding symbol space with the ordinary metric. But these sets are not compact with respect to each metric. We introduce a new topology with respect to which these sets are compact.


37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37B10 Symbolic dynamics
37F99 Dynamical systems over complex numbers
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