Eigenvalues of the Thurston operator. Issue 3 (2nd May 2020)

• Record Type: Journal Article
• Authors: Buff, Xavier; Epstein, Adam L.; Koch, Sarah
• Is Part Of: Journal of topology. Volume 13:Issue 3(2020)
• Page Start: 969
• Page End: 1002
• Publication Date: 2020-05-02
• Subjects: 37F10 -- 37F20 -- 37F45 (primary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12145
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: Let f : C ̂ → C ̂ be a postcritically finite rational map, and let Q ( C ̂ ) be the space of meromorphic quadratic differentials on C ̂ with simple poles. We study the set of eigenvalues of the pushforward operator f ∗ : Q ( C ̂ ) → Q ( C ̂ ) . In particular, we show that when f : C → C is a unicritical polynomial of degree D with periodic critical point, the eigenvalues of f ∗ : Q ( C ̂ ) → Q ( C ̂ ) are contained in the annulus 1 4 D < | λ | < 1 and belong to 1 D U where U is the group of algebraic units.