Geodesic
Many-dimensional solenoid invariant saddle-type sets
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 1, pp. 23-29

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In the paper we construct some example of smooth diffeomorphism of closed manifold. This diffeomorphism has one-dimensional (in topological sense) basic set with stable invariant manifold of arbitrary nonzero dimension and the unstable invariant manifold of arbitrary dimension not less than two. The basic set has a saddle type, i.e. is neither attractor nor repeller. In addition, it follows from the construction that the diffeomorphism has a positive entropy and is conservative (i.e. its jacobian equals one) in some neighborhood of the one-dimensional solenoidal basic set. The construction represented in this paper allows to construct a diffeomorphism with the properties stated above on the manifold that is diffeomorphic to the prime product of the circle and the sphere of codimension one.
Keywords: discrete dynamical system, basic set, separator, topological entropy.
Mots-clés : solenoid 
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     title = {Many-dimensional solenoid invariant saddle-type sets},
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     number = {1},
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     url = {http://geodesic.mathdoc.fr/item/SVMO_2018_20_1_a1/}
}
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E. V. Zhuzhoma; N. V. Isaenkova; V. S. Medvedev. Many-dimensional solenoid invariant saddle-type sets. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 1, pp. 23-29. http://geodesic.mathdoc.fr/item/SVMO_2018_20_1_a1/