Periodic points and smooth rays

Carsten Lunde Petersen*, Saeed Zakeri

*Corresponding author

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Let P: (Formula presented) be a polynomial map with disconnected filled Julia set KP and let z0 be a repelling or parabolic periodic point of P.Weshow that if the connected component of KP containing z0 is non-degenerate, then z0 is the landing point of at least one smooth external ray. The statement is optimal in the sense that all but one cycle of rays landing at z0 may be broken.

TidsskriftConformal Geometry and Dynamics
Udgave nummer8
Sider (fra-til)170-178
Antal sider9
StatusUdgivet - 2021

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