A problem at the interface of differential geometry and dynamical systems
gives rise to the question of what control of solutions of the Riccati
equation {$\dot x+x^2=k(t)$} with positive right-hand side can be obtained
from control of the forcing term k. We show that a known result about
"relative'' pinching is optimal and refine two known theorems. This gives
improved regularity of horospheric foliations and may be of interest in
control or filtering theory.
@article{1067634727,
author = {Gerber, Marlies and Hasselblatt, Boris and Keesing, Daniel},
title = {The Riccati Equation: Pinching of Forcing and Solutions},
journal = {Experiment. Math.},
volume = {12},
number = {1},
year = {2003},
pages = { 129-134},
language = {en},
url = {http://dml.mathdoc.fr/item/1067634727}
}
Gerber, Marlies; Hasselblatt, Boris; Keesing, Daniel. The Riccati Equation: Pinching of Forcing and Solutions. Experiment. Math., Tome 12 (2003) no. 1, pp. 129-134. http://gdmltest.u-ga.fr/item/1067634727/