ON BIFURCATIONS OF TWO-DIMENSIONAL DIFFEOMORPHISMS WITH A HOMOCLINIC TANGENCY TO A SADDLE-NODE FIXED POINT |
| 2 | |
| 2014 |
| scientific article | 517.917 | ||
| 198-209 | homoclinic tangency, saddle-node, bifurcation diagram, first return map, rescaling |
| We study main bifurcations of two-dimensional diffeomorphisms having a quadratic homoclinic tangency to a saddle-node fixed point. The bifurcation diagram for single-round periodic orbits from a small fixed neighborhood of the homoclinic orbit is constructed in the parameter plane. We discuss the relation between the results obtained and the well-known codimension-one bifurcations for the cases of a saddle fixed point with a quadratic homoclinic tangency and a saddle-node fixed point with a transverse homoclinic orbit. |
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