TOPOLOGICAL CHARACTERIZATION OF A SYSTEM WITH HIGH-ORDER SYMMETRIES

Topological characterization of the Lorenz attractor taking into accou nt the two-order equivariance of the vector field has been recently pr oposed by introducing a fundamental domain (typically a wing) and one copy of it. The present paper generalizes this approach to n-order equ ivariant systems. The general procedure is illustrated by taking a spe cific example, namely the so-called proto-Lorenz system which is deriv ed from the Lorenz one. It is shown that symmetric attractors are tile d by n representations of a fundamental domain and that fundamental li nking numbers therefore have to be introduced to conveniently validate the template.