School of Mathematical Sciences Academic Lecture [2025] No.088

(High-level University Construction Series Report No.1110)

Lecture Title: Toy model for bi-critical irrationally indifferent attractors

Lecturer: Jocelyn Russell (Imperial College London)

Lecture Time: September 19, 2025, 15:00–16:00

Venue: Room 1420, Huiwen Building Office Area

Abstract:
This research extends the existing unicritical toy model for irrationally indifferent attractors to the bi-critical case. We introduces a new class of maps parameterized by both the irrational rotation number and an additional parameter, which captures the interaction of two critical points. A key contribution is the construction of a modified change of coordinates that averages two unicritical changes. The model predicts a trichotomy of attractor topologies based on generalized Brjuno and Herman conditions. Future work includes analyzing the behavior of these new functions and determining whether such a renormalization scheme can be realized for actual bi-critical maps.

Lecturer’s Biography:
Jocelyn Russell, PhD student at Imperial College London, mainly engages in research on complex dynamical systems. She has made outstanding contributions in the study of Siegel disks and has been invited to deliver talks at multiple international conferences.

All teachers and students are welcome to attend!

Inviter: Yong Han

School of Mathematical Sciences
September 16, 2025