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Regular version of the site

Article

О числе классов топологической сопряженности диффеоморфизмов Пикстона

Qualitative Theory of Dynamical Systems. 2021. Vol. 20. No. 76. P. 1-15.
Akhmet’ev P., Pochinka O., Medvedev T. V.

For a wide class of dynamical systems known as Pixton diffeomorphisms the topological
conjugacy class is completely defined by the Hopf knot equivalence class, i.e.
the knot whose equivalence class under homotopy of the loops is a generator of the
fundamental group π1(S2×S1).Moreover, any Hopf knot can be realized by a Pixton
diffeomorphism. Nevertheless, the number of the classes of topological conjugacy of
these diffeomorphisms is still unknown. This problem can be reduced to finding topological
invariants of Hopf knots. In the present paper we describe a first order invariant
for these knots. This result allows one to model countable families of pairwise nonequivalent
Hopf knots and, therefore, infinite set of topologically non-conjugate Pixton
diffeomorphisms.