Abstract:
Dynamical systems are considered which are close to systems with a structurally unstable homoclinic curve. A definition of accessibility of a bifuration surface is given, and it is established that a bifurcation surface $H^1$ corresponding to systems with a structurally unstable homoclinic curve will be inaccessible from at least one side. Cases are singled out in which $H^1$ can be the boundary separating Morse–Smale systems from systems with a countable number of periodic motions.
Bibliography: 14 titles.