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A survey on MLC, Rigidity and related topics. (arXiv:1709.09869v1 [math.DS])
来源于:arXiv
The famous MLC Conjecture states that the Mandelbrot set is locally
connected, and it is considered by many to be the central conjecture in
one-dimensional complex dynamics. Among others, it implies density of
hyperbolicity in the quadratic family $\{z^2+c\}_{c\in\mathbb{C}}$. We describe
recent advances on MLC and the relations between MLC, the Density of
Hyperbolicity Conjecture, the Rigidity Conjecture, the No Invariant Line Fields
Conjecture, and the Triviality of Fibers Conjecture. We treat families of
unicritical polynomials and rational maps as well as the exponential family and
families of transcendental maps with finitely many singular values. 查看全文>>