Classification of Complex Polynomial Vector Fields in One Complex Variable
A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.
math.DS↗
arXiv subjects
Bodil Branner
Publications and source records attributed to Bodil Branner.
Homeomorphisms between Limbs of the Mandelbrot Set
Given $p/q$ and $p'/q$ both irreducible, we construct homeomorphisms between the $p/q$ and the $p'/q$ limbs of the Mandelbrot set. This homeomorphisms are not compatible with the dynamics. Moreover, the filled Julia sets of corresponding parameter values are also homeomorphic. All the homeomorphisms above have counterparts on the combinatorial level relating corresponding external arguments, in the dynamical planes as well as in the parameter spaces. Assuming local connectivity of $M$ we may conclude that the constructed homeomorphisms between limbs are compatible with the embeddings of the limbs in the plane.
math.DS↗