Toplogical shooting is a method for proving existence of solutions to certain types of problems in ordinary differential equations. We show how one-dimensional shooting provides an elementary proof that particular equations have solutions which exhibit properties associated with “chaos.” After an introductory illustration of how the method works for a forced pendulum equation, we outline a proof that the Lorenz equations have behavior typical of chaotic systems. Until 1993, there had been no rigorous proof that the Lorenz equations have any kind of chaotic behavior.
No takes yet. Share an insight, caveat, or question.
S. P. Hastings (1994) studied this question.