Abstract
In this paper we discuss the dynamical structure of the rational family \((f_t)\) given by
Each map \(f_t\) has super-attracting immediate basins \(\mathscr {A}_t\) and \(\mathscr {B}_t\) about \(z=0\) and \(z=\infty \), respectively, and two free critical points. We prove that \(\mathscr {A}_t\) (for \(0<|t|\le 1\)) and \(\mathscr {B}_t\) (for \(|t|\ge 1\)) are completely invariant, and at least one of the free critical points is inactive. Based on this separation we draw a detailed picture of the structure of the dynamical and the parameter plane.
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We would like to thank the referee for valuable comments.
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This paper was written during a visit of the CAS supported by the TWA-UNESCO Associateship Scheme.
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Jang, H., Steinmetz, N. On the dynamics of rational maps with two free critical points. Rend. Circ. Mat. Palermo, II. Ser 67, 241–250 (2018). https://doi.org/10.1007/s12215-017-0311-0
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DOI: https://doi.org/10.1007/s12215-017-0311-0