Skip to main content Accessibility help
×
Home

Matings of quadratic polynomials

  • Tan Lei (a1)

Abstract

We apply Thurston's equivalence theory between dynamical systems of post-critically finite branched coverings and rational maps, to try to construct, from a pair of polynomials, a rational map. We prove that given two post-critically finite quadratic polynomials fc: zz2+c and fc:zz2+c′, one can get a rational map if and only if c, c′ are not in conjugate limbs of the Mandelbrot set.

Copyright

References

Hide All
[D]Douady, A.. Systèmes dynamiques holomorphes. Séminaire Bourbaki 599 (1982).
[DH1]Douady, A. & Hubbard, J. H.. Etude dynamique des polynômes complexes I et II, avec la collaboration de P. Lavaurs, Tan Lei et P. Sentenac. Publ. Math. d'Orsay 8402 (1984), 85–04 (1985).
[DH2]Douady, A. & Hubbard, J. H.. A proof of Thurston's topological characterization of rational functions. Preprint, Institut Mittag-Leffler.
[G]Gantmacher, F. R.. Matrix theory. Chelsea Publishing Company, New York 1960.
[H]Hirsch, M. W.. Differential Topology. Springer Verlag, Berlin, 1976.
[La]Lavaurs, P.. Une description combinatoire de l'induction définie par M sur les rationnels à denominateur impair. C. R. Acad. Sc. Paris 303, Série I, no. 4 (1986)
[Le]Levy, S.. Critically finite rational maps. PhD Thesis. Princeton University. Princeton, USA, 1985.
[R1]Rees, M.. A partial description of parameter space of rational maps of degree two: Part I. Preprint, University of Liverpool, UK (1990), Acta Math., to appear.
[R2]Rees, M.. A partial description of parameter space of rational maps of degree two: Part II. Preprint SUNY at Stony Brook, USA (1991).
[R3]Rees, M.. Realization of matings of polynomials as rational maps of degree two. Unpublished manuscript (1986).
[S]Shishikura, M.. On a theorm of M. Rees for matings of polynomials. Preprint, IHES. Bures-sur- Yvette, France (1990).
[ST]Shishikura, M. & Tan, Lei. A family of cubic rational maps and matings of cubic polynomials. Preprint of Max-Planck-Institut für Mathematik. Bonn, Germany 88–50 (1988).
[TA1]Tan, Lei. Accouplements des polynômes quadratiques complexes. C. R. Acad. Sc. Paris 302, Série I, no. 17 (1986), 635638.
[Ta2]Tan, Lei. Accouplements des polynômes complexes. Thése de doctorat de l'Universite de Paris-Sud. Orsay, France (1987).
[Th]Thurston, W.. The combinatorics of iterated rational maps. Preprint, Princeton University, Princeton, USA (1985).
[W]Wittner, B.. On the bifurcation loci of rational maps of degree two. PhD Thesis. Cornell University. Ithaca, USA (1986).
[Y]Yoccoz, J.-C.. Sur la taille des membres de l'ensemble de Mandelbrot. Unpublished manuscript (1986).

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed