SYMMETRICAL FUNCTIONS AND EXACT LYAPUNOV EXPONENTS

Newton's method applied to the elementary symmetric functions of polyn omials generates a class of dynamical systems. These systems have inva riant lines on which the Lyapunov exponents can be found analytically, thus predicting the exact parameter values for which these structures are chaotic attractors (in the sense of Milnor) and precisely when bi furcations, such as blowout, destroy their stability. Often, blowout b ifurcations lead to a behavior called on-off intermittency. We also pr esent evidence that the bursting mechanism of on-off intermittency fre quently occurs in neighborhoods focal points, a common feature of maps that have singularities. Finally, because of an embedding property, t his new class of examples can be extended to construct systems having this bifurcation in higher dimensions. (C) 1998 Elsevier Science B.V.