Ideal systems and connecting orbits
A special class of dynamical systems, called ideal systems, generated by autonomous systems of ordinary differential equations in \(\mathbb R^n\), is considered. For such systems an existence criterion is given for quasi-connecting orbits which connect two critical points. Also, an existence criterion of connecting orbits for general systems is presented. The results obtained extend the results by \textit{Shu-Xiang Yu} [J. Differ. Equations 66, 230--242 (1987; Zbl 0625.34025)] to \(\mathbb R^n\).
scientific article; zbMATH DE number 2130931