Geodesic
Saddle-Type Solenoidal Basis Sets
Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 843-853

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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
Mots-clés : solenoid. 
@article{MZM_2017_101_6_a4,
     author = {E. V. Zhuzhoma and V. S. Medvedev},
     title = {Saddle-Type {Solenoidal} {Basis} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {843--853},
     publisher = {mathdoc},
     volume = {101},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a4/}
}
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E. V. Zhuzhoma; V. S. Medvedev. Saddle-Type Solenoidal Basis Sets. Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 843-853. http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a4/