Isolating segments, fixed point index, and symbolic dynamics

An extension of the recently introduced Srzednicki-Wojcik method for detect ing chaotic dynamics in periodically forced ordinary differential equations is presented. As an application of the method we construct a topological m odel for the planar equation z' =(1 + e(ikt) \ z \(2)) (z) over bar, z is an element of C and we show by a continuation argument that the symbolic dynamics on three symbols for the topological model continues to Eq. (1) for 0 < kappa less t han or equal to 0.495. (C) 2000 Academic Press.