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arXiv · 1910.04705

On the non-monotonicity of entropy for a class of real quadratic rational maps

Khashayar Filom·Kevin M. Pilgrim
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Abstract

We prove that the entropy function on the moduli space of real quadratic rational maps is not monotonic by exhibiting a continuum of disconnected level sets. This entropy behavior is in stark contrast with the case of polynomial maps, and establishes a conjecture on the failure of monotonicity for bimodal real quadratic rational maps of shape $(+-+)$ which was posed in arXiv:1901.03458 based on experimental evidence.

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Khashayar Filom, Kevin M. Pilgrim. 2019-10-10. On the non-monotonicity of entropy for a class of real quadratic rational maps. https://doi.org/10.3934/jmd.2020008

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