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math.DS2025
On the parabolic Fatou domains
Ning Gao, Yan Gao, Wenjuan Peng
Let be a rational map with an infinitely-connected fixed parabolic Fatou domain . We prove that there exists a rational map with a completely invariant parabolic Fatou d…
math.DS2025
Non-recurrent rational maps with disconnected Julia set
Yan Gao, Lele Xu, Luxian Yang
We prove that every wandering exposed Julia component of a rational map is to a singleton, provided that each wandering Julia component containing critical points is non-recurrent.…
math.DS2025
Boundaries of the bounded hyperbolic components of polynomials
Yan Gao, Xiaoguang Wang, Yueyang Wang
In this paper, we study the local connectivity and Hausdorff dimension for the boundaries of the bounded hyperbolic components in the space of polynomials of degree…