Abstract:
We construct a dynamical system in three-dimensional Euclidean space that is described by a system of differential equations with infinitely differentiable right-hand sides, the ordinal number of the central trajectories of which exceeds any given transfinite ordinal of the second class.
\Bibitem{Shi69}
\by L.~P.~Shilnikov
\paper On the work of A.\,G.~Maier on central motions
\jour Mat. Zametki
\yr 1969
\vol 5
\issue 3
\pages 335--339
\mathnet{http://mi.mathnet.ru/mzm6853}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=244558}
\zmath{https://zbmath.org/?q=an:0186.56604}
\transl
\jour Math. Notes
\yr 1969
\vol 5
\issue 3
\pages 204--206
\crossref{https://doi.org/10.1007/BF01388628}
Linking options:
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This publication is cited in the following 3 articles:
L. S. Efremova, “Dynamics of skew products of interval maps”, Russian Math. Surveys, 72:1 (2017), 101–178
L. S. Efremova, “A decomposition theorem for the space of C1-smooth skew products with complicated dynamics of the quotient map”, Sb. Math., 204:11 (2013), 1598–1623
A. I. Shtern, B. A. Efimov, S. Yu. Maslov, V. A. Dushskiǐ, P. I. Lizorkin, Yu. A. Bakhturin, I. Kh. Sabitov, A. N. Parshin, A. V. Prokhorov, I. O. Sarmanov, E. D. Solomentsev, V. V. Fedorchuk, V. V. Afanas'ev, E. G. Goluzina, G. V. Kuz'mina, V. V. Sazonov, I. V. Proskuryakov, A. V. Arkhangel'skiǐ, B. V. Khvedelidze, B. I. Golubov, S. A. Telyakovskiǐ, V. A. Chuyanov, V. E. Plisko, P. S. Modenov, A. B. Ivanov, A. S. Fedenko, V. L. Popov, E. M. Chirka, D. P. Zhelobenko, N. N. Vil'yams, A. V. Chernavskiǐ, O. A. Ivanova, G. A. Meshcheryakov, V. I. Pashkovskiǐ, D. D. Sokolov, E. A. Palyutin, M. Sh. Tsalenko, D. V. Anosov, V. A. Skvortsov, V. A. Eleev, L. D. Kudryavtsev, A. M. Nakhushev, V. M. Millionshchikov, A. P. Soldatov, V. V. Pospelov, E. V. Shikin, E. N. Kuz'min, D. B. Anosov, N. K. Nikol'skiǐ, E. G. Sklyarenko, D. O. Baladze, S. N. Malygin, L. A. Skornyakov, Yu. V. Prokhorov, A. L. Onishchik, L. A. Bokut', A. F. A, Encyclopaedia of Mathematics, 1995, 489