Об устойчивых дугах, соединяющих диффеоморфизмы Палиса на поверхностях

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Об устойчивых дугах, соединяющих диффеоморфизмы Палиса на поверхностях

Динамические системы. 2020. Vol. 10(38). No. 2. P. 139–148.

In this paper, a class of gradient-like diffeomorphisms $f$ on a closed orientable surface is considered, under the assumption that all non-wandering points of $f$ are fixed and have a positive orientation type. The main result is a construction of a stable arc joining two such diffeomorphisms. The diffeomorphisms under the consideration are Palis diffeomorphisms, who highlights their as only surface diffeomorphisms included in topological flows. By S. Newhouse, M. Peixoto, and J. Fleitas result, all Morse-Smale flows on a given manifold are joined by a stable arc. However, this fact cannot be used directly to construct an arc between cascades, since Palis diffeomorphisms are included only in the topological flow. An idea of a stable arc construction between Palis diffeomorphisms is based on the construction of a bifurcation-free arc joining a Palis diffeomorphism with a diffeomorphism that is a one-time shift of a generic gradient flow of a Morse function.

Priority areas: mathematics

Language: English

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Теория динамических систем и ее приложения (2021)

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