# Problem 142

## Primary tabs

Can the  adding machine be an invariant set for a $C^2$ mapping of the 2-disk? of the $n$-disk?

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### See

See

J.M. Gambaudo and C. Tresser, Self-similar constructions in smooth dynamics: rigidity, smoothness and dimension. Comm. Math. Phys. 150 (1992), 45–58.