ON SOME BIFURCATIONS OF TWO-DIMENSIONAL DIFFEOMORPHISMS WITH A HOMOCLINIC TANGENCY TO A NONHYPERBOLIC FIXED POINT |
| 4 | |
| 2014 |
| scientific article | 517.917 | ||
| 476-480 | homoclinic tangency, nonhyperbolic saddle point, first return map, rescaling |
| We study bifurcations in one-parameter family of two-dimensional diffeomorphisms having a quadratic homoclinic tangency to a nonhyperbolic fixed point of an arbitrary finite degeneration. The bifurcation diagram specifies a counting system of intervals accumulating to the origin, each of which has a stable single-round diffeomorphic trajectory. We prove the boundaries of the intervals correspond to bifurcations of single-round periodic orbits. |
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