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Matematicheskie Zametki, 2017, Volume 101, Issue 6, Pages 843–853
DOI: https://doi.org/10.4213/mzm11101 (Mi mzm11101) 		 
Saddle-Type Solenoidal Basis Sets

E. V. Zhuzhoma, V. S. Medvedev

National Research University "Higher School of Economics" (HSE), Moscow
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DOI: https://doi.org/10.4213/mzm11101
Abstract: An example of a diffeomorphism of the $3$-sphere with positive topological entropy which has a one-dimensional solenoidal basis set with a two-dimensional unstable and a one-dimensional stable invariant manifold at each point (in particular, the basis set is neither an attractor nor a repeller) is given. On the basis of this diffeomorphism, a nondissipative fast kinematic dynamo with a one-dimensional invariant solenoidal set is constructed.
Keywords: basis set, solenoid.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-03687-а
16-51-10005-Ko_a
Russian Science Foundation 14-41-00044
This work was supported by the Russian Science Foundation under grant 14-41-00044 and by the Russian Foundation for Basic Research under grants 15-01-03687-a and 16-51-10005-Ko_a. The study was implemented in the framework of the Basis Research Program at the National Research University Higher School of Economics in 2016.
Received: 22.01.2016
Revised: 09.09.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 6, Pages 960–968
DOI: https://doi.org/10.1134/S0001434617050224
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
Citation: E. V. Zhuzhoma, V. S. Medvedev, “Saddle-Type Solenoidal Basis Sets”, Mat. Zametki, 101:6 (2017), 843–853; Math. Notes, 101:6 (2017), 960–968
Citation in format AMSBIB
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