Bifurcations Changing the Type of Heteroclinic Curves of a Morse-Smale 3-Diffeomorphism

Student: Shmukler Valeriia

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Mathematics (Master)

Final Grade: 10

Year of Graduation: 2021

In this paper, we consider the class G of orientation-preserving Morse-Smale diffeomorphisms defined on a closed 3-manifold whose non-wandering set consists of exactly four points of pairwise distinct Morse indices. It is known that the two-dimensional saddle separatrices of any such diffeomorphism always intersect and their intersection necessarily contains non-compact heteroclinic curves, but may also contain compact ones. The main result of this work is the construction of a path in the space of diffeomorphisms connecting the diffeomorphism f from G$ with the diffeomorphism f from G that does not have compact heteroclinic curves.This result is an important step in solving the open problem of describing the topology of 3-manifolds admitting gradient-like diffeomorphisms with wildly embedded saddle separatrices.

Full text (added May 27, 2021)

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