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arXiv · 1307.5278

A finite dimensional approach to Bramham's approximation theorem

Patrice Le Calvez
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Abstract

Using pseudoholomorphic curves techniques from symplectic geometry, Barney Bramham proved recently that every smooth irrational pseudo-rotation of the unit disk is the limit, for the $C^0$ topology, of a sequence of smooth periodic diffeomorphisms. We give here a finite dimensional proof of this result that works in the case where the pseudo-rotation is smoothly conjugate to a rotation on the boundary circle. The proof extends to $C^1$ pseudo rotations and is based on the dynamical study of the gradient flow associated to a generating family of functions given by Chaperon's broken geodesics method.

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Patrice Le Calvez. 2013-07-19. A finite dimensional approach to Bramham's approximation theorem. https://arxiv.org/abs/1307.5278

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