Abstract:
A one-parameter family of smooth vector fields in a space of a high dimension is considered such that for some critical parameter value the corresponding field has a saddle-node cycle (a periodic orbit). The case when the union of the cycle and its homoclinic orbits form a smooth Klein bottle is discussed. The problem consists in the description of the behaviour of the orbit set under the variation of the parameter.
Fulltext:
PDF file (371 kB)
