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Transactions of the Moscow Mathematical Society

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The construction of an energy function for three-dimensional cascades with a two-dimensional expanding attractor


Authors: V. Z. Grines, M. K. Noskova and O. V. Pochinka
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 76 (2015), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2015, 237-249
MSC (2010): Primary 37D20
DOI: https://doi.org/10.1090/mosc/249
Published electronically: November 18, 2015
MathSciNet review: 3468066
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Abstract: In this paper we establish the existence of an energy function for structurally stable diffeomorphisms of closed three-dimensional manifolds whose nonwandering set contains a two-dimensional expanding attractor.


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Additional Information

V. Z. Grines
Affiliation: National Research University Higher School of Economics, Nizhniĭ Novgorod State University
Email: vgrines@yandex.ru

M. K. Noskova
Affiliation: Nizhniĭ Novgorod State University
Email: mknoskova@yandex.ru

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

DOI: https://doi.org/10.1090/mosc/249
Keywords: Energy function, $DA$-diffeomorphism, structurally stable
Published electronically: November 18, 2015
Additional Notes: This research was supported by the Russian Foundation for Basic Research (grants no. 13-01-12452-ofi-m, 15-01-03687-a) and the Russian Science Foundation (grant no. 14-41-00044). This research paper uses the results of the project “Dynamical systems and their applications” carried out in the framework of the Programme of Basic Research of the National Research University Higher School of Economics in 2015.
Article copyright: © Copyright 2015 V. Z. Grines, M. K. Noskova, O. V. Pochinka

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