Geodesic
Nondissipativ kinematic dynamics on lenses
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 2, pp. 53-61

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In the paper we construct smooth (infinitely differentiable) diffeomorphism of three dimensional lens (that is a closed three-manifold that is sheet-finitely covered by three-dimensional sphere). We include a three-dimensional sphere in the list of lens. This mapping has a positive entropy and preserves the volume in some neighborhood of its non-wandering set. We examine the space of diffeomorphisms that are conservative in some neighborhood of their non-wandering sets. In this space there is a neighbourhood consisting of mappings with positive topological entropy (i.e., the diffeomorphism constructed is relatively stable in the class of diffeomorphisms). Due to its properties, the diffeomorphism constructed can act like a model of non-dissipative kinematic fast dynamo. The question is open either the diffeomorphism constructed is the model of a middle or dissipative fast dynamo.
Keywords: diffeomorphism of a solid torus
Mots-clés : solenoid, nondissipative dynamo. 
@article{SVMO_2017_19_2_a3,
     author = {E. V. Zhuzhoma and V. S. Medvedev},
     title = {Nondissipativ kinematic dynamics on lenses},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {53--61},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2017_19_2_a3/}
}
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E. V. Zhuzhoma; V. S. Medvedev. Nondissipativ kinematic dynamics on lenses. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 2, pp. 53-61. http://geodesic.mathdoc.fr/item/SVMO_2017_19_2_a3/