Bifurcation measures and quadratic rational maps

Laura De Marco, Xiaoguang Wang, Hexi Ye

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We study critical orbits and bifurcations within the moduli space M2 of quadratic rational maps, f : P1 → P1. We focus on the family of curves, Per1(λ) ⊂ M2 for λ ε C, defined by the condition that each f ε Per1(λ) has a fixed point of multiplier λ. We prove that the curve Per1(λ) contains infinitely many postcritically finite maps if and only if λ = 0, addressing a special case of Baker and DeMarco ('Special curves and postcritically finite polynomials', Forum of Math. Pi 1 (2013), doi: 10.1017/fmp.2013.2; Conjecture 1.4). We also show that the two critical points of f define distinct bifurcation measures along Per1(λ).

Original languageEnglish (US)
Pages (from-to)149-180
Number of pages32
JournalProceedings of the London Mathematical Society
Volume111
Issue number1
DOIs
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Mathematics(all)

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