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Homoclinic solutions for autonomous dynamical systems in arbitrary dimension. (English) Zbl 0767.34028
Two parameter families of autonomous differential equations are considered, and it is assumed that at the origin of the parameter plane the origin of the phase space is a saddle type equilibrium of the system with a homoclinic trajectory. Conditions are given under which there exist one or more curves in the parameter plane at the points of which the system still has homoclinic trajectories. The Lyapunov-Schmidt method is applied. The results are illustrated by several examples.
MSC:
34C37Homoclinic and heteroclinic solutions of ODE
37-99Dynamic systems and ergodic theory (MSC2000)