Horn maps of semi-parabolic Hénon maps
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DOI: 10.1007/s00208-024-03085-3
Abstract: We prove that horn maps associated to quadratic semi-parabolic fixed points of Hénon maps, first introduced by Bedford, Smillie, and Ueda, satisfy a weak form of the Ahlfors island property. As a consequence, two natural… read more here.
Keywords: semi parabolic; horn maps; non maps; usepackage ... See more keywords
A structure theorem for semi-parabolic Hénon maps
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DOI: 10.1016/j.aim.2019.05.001
Abstract: Consider the parameter space $\mathcal{P}_{\lambda}\subset \mathbb{C}^{2}$ of complex H\'enon maps $$ H_{c,a}(x,y)=(x^{2}+c+ay,ax),\ \ a\neq 0 $$ which have a semi-parabolic fixed point with one eigenvalue $\lambda=e^{2\pi i p/q}$. We give a characterization of those H\'enon… read more here.
Keywords: semi parabolic; julia set; structure theorem; parabolic non ... See more keywords