MSC2010 37C70

### Nondissipativ kinematic dynamics on lenses

#### E. V. Zhuzhoma1, V. S. Medvedev2

Annotation In the paper, one constructs smooth (infinitely many differentiable) diffeomorphism of three dimensional lens (a closed three-manifold that is sheet-finitely covered by three-dimensional sphere) which has a positive entropy and keeps the volume in some neighborhood of its non-wandering set (note that in the list of lens, we include a three-dimensional sphere). In addition, there is a neighborhood in the space of diffeomorphisms that is conservative in some neighborhood of its non-wandering set which is consisted of diffeomorphisms with a positive entropy (i.e., the diffeomorphism constructed is relatively stable in the class of diffeomorphisms). Due to the properties, the diffeomorphism constructed can be a model of non-dissipative kinematic fast dynamo (the open question is either the diffeomorphism constructed the model of a middle or dissipative fast dynamo). diffeomorphism of a solid torus, solenoid, nondissipativ dynamics

1Evgeny V. Zhuzhoma, Professor of the Department of Fundamental Mathematics, Research Institute of Higher School of Economics (603155, Russia,   Nizhny Novgorod, zhuzhomazhul. Bolshaya Pecherskaya, 25), Dr. Sci. (Physics and Mathematics), ORCID:http://orcid.org/0000-0001-8682-7591, zhuzhoma@mail.ru

2Vladislav S. Medvedev, researcher TAPRADESS laboratory, NIU Higher School of Economics (603155, Russia,   Nizhny Novgorod, Ul. Bolshaya Pecherskaya, 25), PhD (Physics and Mathematics), ORCID:http://orcid.org/0000-0001-6369-0000, vmedvedev@hse.ru

Citation: E. V. Zhuzhoma, V. S. Medvedev, "[Nondissipativ kinematic dynamics on lenses]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:2 (2017) 53–61 (In Russian)

DOI 10.15507/2079-6900.19.201701.053-061