The Riccati Equation: Pinching of Forcing and Solutions

Abstract

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.