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arXiv:1910.04705 [math.DS]AbstractReferencesReviewsResources

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

Khashayar Filom, Kevin M. Pilgrim

Published 2019-10-10Version 1

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.

Comments: 30 pages, 9 figures
Categories: math.DS
Subjects: 37B40, 37E05, 37F10, 37F30, 37F45
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