Year: 2025
Type: article
Abstract: We consider rational maps f f on the Riemann sphere C ^ \widehat {\mathbb {C}} with an f f -invariant set P ⊂ C ^ P\subset \widehat {\mathbb {C}} of four marked points containing the postcritical set of f f . We show that the dynamics of the corresponding Thurston pullback map σ f \sigma _f on the completion T P ¯ \overline {\mathcal {T}_P} of the associated Teichmüller space T P \mathcal {T}_P with respect to the Weil–Petersson metric is easy to understand when T P ¯ \overline {\mathcal {T}_P} admits a cover by sets with good combinatorial and dynamical properties. In particular, the map f f has a finite global curve attractor in this case. Using a result by Eremenko and Gabrielov, we also show that if P P contains all critical points of f f and each point in P P is periodic, then such a cover of
DOI: 10.1090/bproc/274
Authors: Mario Bonk, Mikhail Hlushchanka, Russell Lodge
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $750
OpenAlex ID: W4416967220