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Monotonicity of entropy for unimodal real quadratic rational maps

We show that the topological entropy is monotonic for unimodal interval maps which are obtained from the restriction of quadratic rational maps with real coefficients. This is done by ruling out the existence of certain post-critical curves in the moduli space of aforementioned maps, and confirms a conjecture made in [Fil19] based on experimental evidence.

preprint2020arXivOpen access
Yan Gao
math.DS
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Yan Gao

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