Abstract:
It is shown that in a neighborhood of a trajectory which is doubly asymptotic to a rough state of equilibrium of saddle-focus type, under addition assumptions on the dynamical system, there exists a subsystem whose trajectories are in one-to-one correspondence with a set which is the quotient space of a topological Bernoulli process with an infinite set of symbols.
Bibliography: 10 titles.
Citation:
L. P. Shilnikov, “A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type”, Math. USSR-Sb., 10:1 (1970), 91–102
\Bibitem{Shi70}
\by L.~P.~Shilnikov
\paper A~contribution to the problem of the structure of an extended neighborhood of a~rough equilibrium state of saddle-focus type
\jour Math. USSR-Sb.
\yr 1970
\vol 10
\issue 1
\pages 91--102
\mathnet{http://mi.mathnet.ru/eng/sm3363}
\crossref{https://doi.org/10.1070/SM1970v010n01ABEH001588}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=259275}
\zmath{https://zbmath.org/?q=an:0193.05301|0216.11201}
Linking options:
https://www.mathnet.ru/eng/sm3363
https://doi.org/10.1070/SM1970v010n01ABEH001588
https://www.mathnet.ru/eng/sm/v123/i1/p92
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