A proof that the Lorenz equations have a homoclinic orbit (Q1336342)

This is one of several papers the goal of which consists in a rigorous verification of the conclusions obtained with the assistance of computers. Here a shooting-type method is applied to prove analytically the existence of a homoclinic orbit, namely a nonconstant solution of the Lorenz system, tending to the same equilibrium point \((0,0,0)\) at \(\pm\infty\). The associated set of parameter values is open.