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arXiv · 1603.01609

On parabolic external maps

Luna Lomonaco·Carsten Petersen·Weixiao Shen
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Abstract

We prove that any $C^{1+BV}$ degree $d \geq 2$ circle covering $h$ having all periodic orbits weakly expanding, is conjugate in the same smoothness class to a metrically expanding map. We use this to connect the space of parabolic external maps (coming from the theory of parabolic-like maps) to metrically expanding circle coverings.

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Luna Lomonaco, Carsten Petersen, Weixiao Shen. 2016-03-04. On parabolic external maps. https://doi.org/10.3934/dcds.2017220

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