Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three invariants of strange attractors derived through hypergeometric
  entropy   A new description of strange attractor systems through three geometrical and
dynamical invariants is provided. They are the correlation dimension
($\mathcal{D}$) and the correlation entropy ($\mathcal{K}$), both having
attracted attention over the past decades, and a new invariant called the
correlation concentration ($\mathcal{A}$) introduced in the present study. The
correlation concentration is defined as the normalised mean distance between
the reconstruction vectors $\{\boldsymbol{X}_{i}\}$, evaluated by the
underlying probability measure on the infinite-dimensional embedding space.
These three invariants determine the scaling behaviour of the system's
R\'{e}nyi-type extended entropy, which involves a kernel function of the form
$e^{-\rho\|\boldsymbol{X}_{i}-\boldsymbol{X}_{j}\|}$ with $\rho$ a positive
spectral parameter. The entropy function is modelled by Kummer's confluent
hypergeometric function, which reproduces the known scaling behaviours of
$\mathcal{D}$ and $\mathcal{K}$ in the "microscopic" limit $\rho\to\infty$
while exhibiting a new scaling behaviour of $\mathcal{A}$ in the other,
"macroscopic" limit $\rho\to 0$. The three invariants are estimated
simultaneously via nonlinear regression analysis without needing separate
estimations for each invariant. The proposed method is verified through
simulations in both discrete (logistic and H\'{e}non maps) and continuous
(Lorenz, R\"{o}ssler, Duffing-Ueda and Langford attractors) systems. These
results provide an improved understanding of the complex spatiotemporal
properties of the chaotic system.

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The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga