Trees and the Dynamics of Polynomials
| Title: | Trees and the Dynamics of Polynomials |
| Author: |
McMullen, Curtis T.; DeMarco, Laura G.
Note: Order does not necessarily reflect citation order of authors. |
| Citation: | DeMarco, Laura G., and Curtis T. McMullen. 2008. Trees and the dynamics of polynomials. Annales Scientifiques de l'École Normale Supérieure 41: 337-383. |
| Full Text & Related Files: |
McMullen_TreesDynamPoly.pdf (428.9Kb; PDF) 
|
| Abstract: | In this paper we study branched coverings of metrized, simplicial trees F : T → T which arise from polynomial maps f : C → C with disconnected Julia sets. We show that the collection of all such trees, up to scale, forms a contractible space PTD compactifying the moduli space of polynomials of degree D; that F records the asymptotic behavior of the multipliers of f; and that any meromorphic family of polynomials over Δ* can be completed by a unique tree at its central fiber. In the cubic case we give a combinatorial enumeration of the trees that arise, and show that PT3 is itself a tree. |
| Published Version: | http://smf.emath.fr/Publications/ |
| Terms of Use: | This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP |
| Citable link to this page: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:3445096 |
This item appears in the following Collection(s)
-
FAS Scholarly Articles [5138]
Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
Contact administrator regarding this item (to report mistakes or request changes)
