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Necessary and sufficient conditions for the topological conjugacy of 3-diffeomorphisms with heteroclinic tangencies


Authors: T. M. Mitryakova and O. V. Pochinka
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 77 (2016), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2016, 69-86
MSC (2010): Primary 37D20
DOI: https://doi.org/10.1090/mosc/253
Published electronically: November 28, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider a class of three-dimensional diffeomorphisms that differ from gradient-like systems through the presence of heteroclinic tangencies. It is well known that such cascades are not structurally stable. However, here we find a complete system of topological invariants for a certain meaningful class of such diffeomorphisms.


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Additional Information

T. M. Mitryakova
Affiliation: Department of Mechanics and Mathematics, Nizhnii Novgorod State University, Nizhmii Novgorod, 603950 Russian Federation
Email: tatiana.mitryakova@yandex.ru

O. V. Pochinka
Affiliation: National Research University Higher School of Economics
Email: olga-pochinka@yandex.ru

DOI: https://doi.org/10.1090/mosc/253
Keywords: Heteroclinic tangencies, moduli of topological conjugacy, discrete dynamical systems
Published electronically: November 28, 2016
Additional Notes: This research was supported by the Programme for Basic Research of the National Research University Higher School of Economics in 2016 (project no. 98 “Topological methods in dynamics”), the Russian Science Foundation (project no. 15-01-03689-a), and the research work in accordance with the commission 2014/134 for performing state work in the sphere of scientific activity in the framework of the basic part of the state commission of the Ministry for Education and Science of Russia for 2014–2016 (Nizhnii Novgorod State University)
Article copyright: © Copyright 2016 American Mathematical Society

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