  The defining feature of chaos is its hypersensitivity to small perturbations.
However, we report a stability of branched flow against large perturbations
where the classical trajectories are chaotic, showing that strong perturbations
are largely ignored by the quantum dynamics. The origin of this stability is
accounted for by the piecewise nature of the interference, which is largely
ignored by the traditional theory of scattering. Incorporating it into our
theory, we introduce the notion of piecewise classical stable paths(PCSPs). Our
theory shall have implications for many different systems, from electron
transport in nanostructures, light propagation in nonhomogeneous photonic
structures to freak wave formations in oceans.
