Abstract
Abstract
The monotonicity of entropy is investigated for real quadratic rational maps on the real circle
R
∪
{
∞
}
based on the natural partition of the corresponding moduli space
M
2
(
R
)
into its monotonic, covering, unimodal and bimodal regions. Utilizing the theory of polynomial-like mappings, we prove that the level sets of the real entropy function
h
R
are connected in the (−+−)-bimodal region and a portion of the unimodal region in
M
2
(
R
)
. Based on the numerical evidence, we conjecture that the monotonicity holds throughout the unimodal region, but we conjecture that it fails in the region of (+−+)-bimodal maps.
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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