Nested Cantor sets

Pierre Berger; Carlos Gustavo Moreira

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arXiv · 1303.0971

Nested Cantor sets

Pierre Berger·Carlos Gustavo Moreira

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Abstract

We give sufficient conditions for two Cantor sets of the line to be nested for a positive set of translation parameters. This problem occurs in diophantine approximations. It also occurs as a toy model of the parameter selection for non-uniformly hyperbolic attractors of the plane. For natural Cantors sets, we show that this condition is optimal.

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Pierre Berger, Carlos Gustavo Moreira. 2013-03-05. Nested Cantor sets. https://arxiv.org/abs/1303.0971

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