Saddle-Type Solenoidal Basis Sets

E. V. Zhuzhoma ; V. S. Medvedev

Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 843-853.

Résumé

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.

Détail

Keywords: basis set
Mots-clés : solenoid.

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