论文标题
与模块化组III的交配二次图：模块化mandelbrot集
Mating quadratic maps with the modular group III: The modular Mandelbrot set
论文作者
论文摘要
我们证明，在连接性基因座$ \ MATHCAL {M}_γ$之间存在同质形态$χ$，用于家庭$ \ Mathcal {F} _a $ of $（2：2）$（2：2）$ HOLOMORPHIC对应关系，由Bullett和Penrose引入了由Bullet和Penrose引入的，以及Parabolic Mandelbrot us us parabolic Mandelbrot set $ \ nathcal $ \ \ mathcalcal} $}同构$χ$是动态的（$ \ nathcal {f} _a $是$ psl（2，2，\ mathbb {z}）$和$ p_ {χ（a）} $之间的交配，它是$ \ nathcal {m}_γ$的内部范围，并在纽约的内部相同，并在家中均延长了一个习惯。参数模量空间。 在Petersen和Roesch最近证明$ \ MATHCAL {M} _1 $对经典Mandelbrot Set $ \ Mathcal {M Mathcal {M} $的同型是同质的，我们推断出$ \ Mathcal {M}_γ$是同型对$ \ \ nathcal {m Mathcal {m} $。
We prove that there exists a homeomorphism $χ$ between the connectedness locus $\mathcal{M}_Γ$ for the family $\mathcal{F}_a$ of $(2:2)$ holomorphic correspondences introduced by Bullett and Penrose, and the parabolic Mandelbrot set $\mathcal{M}_1$. The homeomorphism $χ$ is dynamical ($\mathcal{F}_a$ is a mating between $PSL(2,\mathbb{Z})$ and $P_{χ(a)}$), it is conformal on the interior of $\mathcal{M}_Γ$, and it extends to a homeomorphism between suitably defined neighbourhoods in the respective one parameter moduli spaces. Following the recent proof by Petersen and Roesch that $\mathcal{M}_1$ is homeomorphic to the classical Mandelbrot set $\mathcal{M}$, we deduce that $\mathcal{M}_Γ$ is homeomorphic to $\mathcal{M}$.
