8 papers
On the Abel-Nörlund-Voronoi summability and instability of rational maps
Carlos Cabrera, Peter Makienko, Alfredo Poirier
We investigate the connection between the instability of rational maps and summability methods applied to the spectrum of a critical point on the Julia set of a given rational map.
Hyperbolic Components
John Milnor, Alfredo Poirier
Consider polynomial maps $f:\C\to\C$ of degree , or more generally polynomial maps from a finite union of copies of $\C$ to itself. In the space of suitably normalized maps…
Coexistence of critical orbit types in sub-hyperbolic polynomial maps
Alfredo Poirier
We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynom…
On postcritically finite polynomials, part 2: Hubbard trees
Alfredo Poirier
We provide an effective classification of postcritically finite polynomials as dynamical systems by means of Hubbard Trees. This can be viewed as an application of the results deve…
On postcritically finite polynomials, part 1: critical portraits
Alfredo Poirier
We extend the work of Bielefeld, Fisher and Hubbard on Critical Portraits to the case of arbitrary postcritically finite polynomials. This determines an effective classification of…
Hubbard forests
Alfredo Poirier
The theory of Hubbard trees provides an effective classification of non-linear post-critically finite polynomial maps from \C to itself. This note will extend this classification t…