Parabolic bifurcation loci in the spaces of rational functions

We give a geometric description of the parabolic bifurcation locus in the space Rat d of all rational functions on P 1 of degree d > 1, generalising the study by Morton and Vivaldi in the case of monic polynomials. The results are new even for quadratic rational functions.

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Bibliographische Detailangaben
Veröffentlicht in:	Nonlinearity 2022-11, Vol.35 (11), p.5938-5962
1. Verfasser:	Okuyama, Yûsuke
Format:	Artikel
Sprache:	eng
Schlagworte:	complex dynamics cyclotomic polynomial dynatomic polynomial multiplier polynomial parabolic bifurcation hypersurface parabolic bifurcation locus potential theory
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Beschreibung
Zusammenfassung:	We give a geometric description of the parabolic bifurcation locus in the space Rat d of all rational functions on P 1 of degree d > 1, generalising the study by Morton and Vivaldi in the case of monic polynomials. The results are new even for quadratic rational functions.
ISSN:	0951-7715 1361-6544
DOI:	10.1088/1361-6544/ac8041