Chaplygin sleigh in the quadratic potential field

We study numerically the dynamics of Chaplygin sleigh under the action of the quadratic potential field. In contrast with the free Chaplygin sleigh our mechanical model manifests a complex behaviour: conservative-like chaotic regimes at low energies, coexistent pairs of chaotic attractors and repellers, mapping to each other by time-reversal symmetry, and the recently discovered phenomenon of attractor and repeller intersection, at high energies. We demonstrate that the development of attractors and repellers corresponds to a period doubling scenario, followed by their collision and instant increase in size