Skipping and snake orbits of electrons: singularities and catastrophes
  Near the sample edge, or a sharp magnetic field step the drift of two-dimensional electrons in a magnetic field has the form of skipping/snake orbits. We show that families of skipping/snake orbits of electrons injected at one point inside a 2D metal generically exhibit caustics folds, cusps and cusp triplets, and, in one extreme case, a section of the batterfly bifurcation. Periodic appearance of singularities along the $\pm B$-interface leads to the magneto-oscillations of nonlocal conductance in multi-terminal electronic devices. 
Nathan Davies, Aavishkar A. Patel, Alberto Cortijo, Vadim Cheianov,   Francisco Guinea, Vladimir I. Fal'ko
cond-mat.mes-hall