Cantor Sets, Binary Trees and Lipschitz Circle Homeomorphisms
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چکیده
We define the notion of rotations on infinite binary trees, and construct an irrational tree rotation with bounded distortion. This lifts naturally to a Lipschitz circle homeomorphism having the middle-thirds Cantor set as its minimal set. This degree of smoothness is best possible, since it is known that no C1 circle diffeomorphism can have a linearly self-similar Cantor set as its minimal set.
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تاریخ انتشار 2002