Conventional multipliers for homoclinic orbits

In this work we introduce and describe conventional multipliers, a new characteristic of homoclinic orbits of saddle-node type periodic trajectories. We prove existence and smooth dependence of conventional multipliers on the initial point. We show that multipliers of periodic trajectories arising from the homoclinic ones as a result of the saddle-node bifurcation are close to the conventional multipliers. As an application we study behavior of a circle map inside the 'Arnold tongues'.