The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifically by his seminal work initiated by Cartwright and Littlewood .
Ang bakalan mapa ay direkta stimulated by Levinson ng pananaliksik sa sapilitang panaka-oscillations ng Van der Pol osileytor, at partikular na sa pamamagitan ng kanyang matagumpay na sinimulan sa pamamagitan ng trabaho Cartwright at Littlewood.