A shooting approach to chaos in the Lorenz equations
The authors prove that under certain conditions on sign changes for one variable \(x\) and its derivative \(x'\) the Lorenz equations support a form of chaos. The conditions have been verified numerically in a different paper using interval arithmetic for a particular set of parameter values. After choosing a proper line segment it is shown that for any sequence \(S = \{\sigma_j\}\) of natural numbers one can construct initial conditions on this segment, such that the number of sign changes of \(x'\) between consecutive zeros of \(x\) is in one-to-one correspondence with \(\sigma_j\).
scientific article; zbMATH DE number 881700