A new method of detection of chaos in dynamical systems generated by t
ime-periodic nonautonomous differential equations is presented. It is
based on the existence of some sets (called periodic isolating segment
s) in the extended phase space, satisfying some topological conditions
. By chaos we mean the existence of a compact invariant set such that
the Poincare map is semiconjugated to the shift on two symbols and the
counterimage (by the semiconjugacy) of any periodic point in the shif
t contains a periodic point of the Poincare map. As an application we
prove that the planar equation z = (1 + e(t phi t) \z\(2))(z) over bar
generates chaotic dynamics provided 0 < phi less than or equal to 1/2
88. (C) 1997 Academic Press.