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Mat. Zametki, 2017, Volume 101, Issue 6, Pages 843–853 (Mi mz11101)  

Saddle-Type Solenoidal Basis Sets

E. V. Zhuzhoma, V. S. Medvedev

National Research University "Higher School of Economics" (HSE), Moscow

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.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11101

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English version:
Mathematical Notes, 2017, 101:6, 960–968

Bibliographic databases:

UDC: 517.938
Received: 22.01.2016
Revised: 09.09.2016

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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