Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
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A calculation of periodic data of surface diffeomorphisms with one saddle orbit.

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Published Sep 15, 2018
DOI https://doi.org/10.15673/tmgc.v11i2.1025

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Олена В'ячеславівна Ноздрінова
National Research University “Higher School of Economics”
http://orcid.org/0000-0001-5209-377X
Ольга Віталіївна Починка
National Research University “Higher School of Economics”
http://orcid.org/0000-0002-6587-5305

Abstract

In the paper it is proved that any orientable surface admits an orientation-preserving diffeomorphism with one saddle orbit. It distinguishes in principle the considered class of systems from source-sink diffeomorphisms existing only on the sphere. It is shown that diffeomorphisms with one saddle orbit of a positive type on any surface have exactly three node orbits. In addition, all possible types of periodic data for such diffeomorphisms are established. Namely, formulas are found expressing the periods of the sources through the periods of the sink and the saddle.
Keywords:
periodic data, surface

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How to Cite
Ноздрінова, О., & Починка, О. (2018). A calculation of periodic data of surface diffeomorphisms with one saddle orbit. Proceedings of the International Geometry Center, 11(2). https://doi.org/10.15673/tmgc.v11i2.1025
Issue
Vol 11 No 2 (2018)
Section
Papers

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