ABSTRACT
Consider the solutions x( tj to , xo) of an arbitrary system of equations start ing from the initial set Ho at to . For t > 0, let Ht = {x(t; to , xo ) : Xo E Ho} . Its Lebesque measure p,(Ht} is called the phase-volume. Evolution of the phase-volume can yield valuable information about the behavior of solu tions. This method is often applied to investigate instability properties of both linear and nonlinear systems (see [5, 7, 8, 9, 1 1 , 1 2] ) because if p,(Ht ) -. 00 as t � 00, then the system possesses certain instability proper ties. On the other hand, if p,(Ht } tends to zero, some attractivity properties
can be concluded, although we may not be able to deduce the asymptotic stability or even just stability of the system.
