Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the non-monotonicity of entropy for a class of real quadratic
  rational maps   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.

13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th