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I recently learned about the poincare-birkhoff fixed point theorem, and was wondering if there is a simple example of an area-preserving (or some weaker assumptions) twist map on the annulus which has exactly two fixed points.

Plus, I am looking for a natural class of examples of such maps that has only a few fixed points.

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The Chirikov Map, also know as Standard Map, is a twist map with two fixed points.

Follow the link below

http://mathworld.wolfram.com/StandardMap.html

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