Conventional multipliers for homoclinic orbits
V Afraimovich; W S Liu; T Young; V Afraimovich; Georgia Institute of Technology, Center for Dynamical Systems and Nonlinear Studies and School of Mathematics, Atlanta, GA 30332-0190, USA; W S Liu; Georgia Institute of Technology, Center for Dynamical Systems and Nonlinear Studies and School of Mathematics, Atlanta, GA 30332-0190, USA; T Young; Georgia Institute of Technology, Center for Dynamical Systems and Nonlinear Studies and School of Mathematics, Atlanta, GA 30332-0190, USA
Журнал:
Nonlinearity
Дата:
1996-01-01
Аннотация:
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'.
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