A GEOMETRIC-METHOD FOR DETECTING CHAOTIC DYNAMICS

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.