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Distortion elements in the group of diffeomorphisms of the 2-sphere
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 46 / Issue 5 / May 2026
- Published online by Cambridge University Press:
- 20 February 2026, pp. 1155-1165
- Print publication:
- May 2026
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- Article
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We characterize dynamics of every distortion element in the group of diffeomorphisms of the 2-sphere that has at least two fixed points and another recurrent point. The key result is that if f is such a diffeomorphism, then the homeomorphism
$\check {f}_{\mathrm { ann}}$, which is a lift of the homeomorphism of the closed annulus 
$\overline {\mathcal {A}}$ obtained from 
$\mathbb {S}^2$ by blowing up two fixed points of f to the universal covering space of 
$\overline {\mathcal {A}}$, has a unique rotation number. Moreover, we find the differential of such a distortion element in the group of diffeomorphisms of the 2-sphere at each fixed point up to conjugacy.
