Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decreasing families of dynamically determined intervals in the power-law
  family   We study the rate of growth of ratios of intervals delimited by the
post-critical orbit of a map in the quasi-quadratic family $x\mapsto
-|x|^\alpha +a.$ The critical order $\alpha$ is an arbitrary real number
$\alpha>1.$ The range of the parameter $a$ is confined to an interval
$(1,a_{\alpha})$ of length depending on the critical order. We prove that in
every power-law family there is a unique parameter $p_{\alpha}$ corresponding
to the kneading sequence $RLRRRLRC.$ Subsequently, we obtain monotonicity
results concerning ratios of all intervals labeled by infinite post-critical
orbit in the case of the kneading sequence $RLRL...$ This extends the results
from \cite{P}, via refinement of the tools based on special properties of
power-law mappings in non-euclidean metric.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga