Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, Tome 36 (2010), pp. 112-124
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D. Li. On a class of strongly contractive quadratic recurrent systems. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, Tome 36 (2010), pp. 112-124. http://geodesic.mathdoc.fr/item/CMFD_2010_36_a8/
@article{CMFD_2010_36_a8,
author = {D. Li},
title = {On a~class of strongly contractive quadratic recurrent systems},
journal = {Contemporary Mathematics. Fundamental Directions},
pages = {112--124},
year = {2010},
volume = {36},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CMFD_2010_36_a8/}
}
TY - JOUR
AU - D. Li
TI - On a class of strongly contractive quadratic recurrent systems
JO - Contemporary Mathematics. Fundamental Directions
PY - 2010
SP - 112
EP - 124
VL - 36
UR - http://geodesic.mathdoc.fr/item/CMFD_2010_36_a8/
LA - ru
ID - CMFD_2010_36_a8
ER -
%0 Journal Article
%A D. Li
%T On a class of strongly contractive quadratic recurrent systems
%J Contemporary Mathematics. Fundamental Directions
%D 2010
%P 112-124
%V 36
%U http://geodesic.mathdoc.fr/item/CMFD_2010_36_a8/
%G ru
%F CMFD_2010_36_a8
We consider a class of nonlinear recurrent systems of the form $\Lambda_p=\frac1p\sum_{p_1=1}^{p-1} f(\frac {p_1}p)\Lambda_{p_1}\Lambda_{p-p_1}$, $p>1$, where f is a given function on the interval $[0,1]$ and $\Lambda_1=x$ is an adjustable real-valued parameter. Under some suitable assumptions on the function $f$, we show that there exists an initial value $x^*$ for which $\Lambda_p=\Lambda_p(x^*)\to\mathrm{const}$ as $p\to\infty$. More precise asymptotics of $\Lambda_p$ is also derived.
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