Loss of Determinacy at Small Scales, with Application to Multiple Timescale and Nonsmooth Dynamics

A singularity is described that creates a forward time loss of determinacy in two-timescale system, the limit where timescale separation large. We describe how situation can arise dynamical system two fast variables and three slow or parameters, with weakly coupling between variables. wide set initial conditions enters [Formula: see text]-neighborhood singularity, explodes back out it to fill large region phase space, all finite time. The scenario has particular significance application piecewise-smooth systems, arises blow up dynamics at discontinuity followed by abrupt recollapse solutions “hide” determinacy, yet leave behind remnant global dynamics. This constitutes generalization “micro-slip” phenomenon found recently spring-coupled blocks, whereby coupled oscillators undergo unpredictable stick-slip-stick sequences instigated higher codimension form singularity. indeterminacy localized brief slips events, but remains evident indeterminate sequencing near-simultaneous multiple blocks.