Rigidity of J-rotational rational maps and critical quasicircle maps
Abstract
We present a number of rigidity results concerning holomorphic dynamical systems admitting rotation quasicircles. Firstly, we show the absence of line fields on the Julia set of any rational map that is geometrically finite away from a number of rotation quasicircles with bounded type rotation number. As an application, we prove combinatorial rigidity associated to the problem of degeneration of Herman rings of the simplest configuration. Secondly, we extend a result of de Faria and de Melo on the C 1 + α C^{1+\alpha } rigidity of critical circle maps with bounded type rotation number to a larger class of dynamical objects, namely critical quasicircle maps . Unlike critical circle maps, critical quasicircle maps may have imbalanced inner and outer criticalities. As a consequence, we prove dynamical universality and exponential convergence of renormalization towards a horseshoe attractor.
Fields of Study & Subjects
Quantum chaos and dynamical systems
Mathematical Dynamics and Fractals
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 379
- Issue
- 4
- Pages
- 2507–2567
- Publication date
- 21 January 2026
- Language
- EN