A GENERIC, HARD TRANSITION TO CHAOS

A hard-in-amplitude transition to chaos in a class of dissipative flow s of broad applicability is presented. For positive values of a parame ter Gamma, no matter how small, a fully developed chaotic attractor ex ists within some domain of additional parameters, whereas no chaotic b ehavior exists for Gamma less than or equal to 0. As Gamma is made pos itive, an unstable fixed point reaches an invariant plane to enter a p hase half-space of physical solutions; the ghosts of a line of fixed p oints and a rich heteroclinic structure existing at Gamma = 0 make the limits t --> +infinity, Gamma --> +0 non-commuting, and allow an exac t description of the chaotic flow. The formal structure of flows that exhibit the transition is determined. A subclass of such flows (couple d oscillators in near-resonance at any 2 : q frequency ratio, with Gam ma representing linear excitation of the first oscillator) is fully an alysed.