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MSC2010 37B35

A scenario of the homotopy type changing of the invariant saddle manifold closure

E. V. Nozdrinova1

AnnotationThe paper deals with surface gradient-like diffeomorphisms. The closures of the invariant manifolds of saddle points of such systems contain nodal points in their closure. In the case when there is only one such point, the closure of the invariant manifold is a closed curve that is homeomorphic to the circle. In a general case the conjugating homeomorphism changes the homotopy type of the closed curve, while the diffeomorphisms themselves may remain in the same isotopic class. This means that in the space of diffeomorphisms two such systems are connected by an arc, but every such arc necessarily undergoes bifurcations. In this paper, we describe a scenario for changing the homotopy type of the closure of the invariant saddle manifold. Moreover, the constructed arc is stable in the space of diffeomorphisms.
Keywordsstable arc, saddle-node, homotopy type of curve, bifurcation, manifold

1Elena V. Nozdrinova, Research Fellow, International Laboratory of Dynamical Systems and Applications, National Research University Higher School of Economics (25/12 Bolshaya Pecherskaya St., Nizhnii Novgorod 603155, Russia), ORCID: http://orcid.org/0000-0001-5209-377X, maati@mail.ru

Citation: E. V. Nozdrinova, "[A scenario of the homotopy type changing of the invariant saddle manifold closure]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,22:3 (2020) 306–318 (In Russian)

DOI 10.15507/2079-6900.22.202003.306-318