Dimension estimate of the global attractor for resonant motion of a spherical pendulum

By Isamu Ohnishi

Proc. Japan Acad. Ser. A Math. Sci., Volume 68, Number 9 (1992), 302-306.

The Abstract is the following: 

Miles derived a system (SP). It describes the motion of a lightly damped spherical pendulum, which is forced to oscillate horizontally in the neighborhood of resonance.  The aim of this paper is to estimate an upper bound for the dimension of X  analytically. Basically we make use of the Kaplan-Yorke formula. This formula connects the upper bound with the Lyapunov exponents. This was conjectured by Kaplan and Yorke and proved by Constantin and Foias. In Eden, Foias and Temam, this enables to estimate the dimension of a global attractor for the Lorenz system. (SP) consists of four equations unlike the Lorenz system. We adopt the technique used in Ishimura and Nakamura.

Onishi : Dimension estimate of the global attractor for resonant motion of a spherical pendulum

©1993 The Japan Academy-All rights reserved.