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This article is cited in 12 scientific papers (total in 12 papers)
On attainable transitions from Morse–Smale systems to systems with many periodic motions
V. S. Afraimovich, L. P. Shilnikov
Abstract:
In this paper it is proved that with the disappearance of equilibrium states of the type saddle-saddle there appear singular sets homeomorphic to a suspension over a certain topological Markov chain. It is established that the corresponding bifurcation surface can separate Morse–Smale systems from systems with a countable set of periodic motions and is $\Omega$-attainable on both sides. On the basis of the results obtained a description is given of the structure of basic sets connected with the appearance of homoclinic curves. Cases are indicated when the description of the structure of the neighborhood of a homoclinic curve coincides with the description of a basic set.
Received: 19.09.1973
Citation:
V. S. Afraimovich, L. P. Shilnikov, “On attainable transitions from Morse–Smale systems to systems with many periodic motions”, Izv. Akad. Nauk SSSR Ser. Mat., 38:6 (1974), 1248–1288; Math. USSR-Izv., 8:6 (1974), 1235–1270
Linking options:
https://www.mathnet.ru/eng/im2009https://doi.org/10.1070/IM1974v008n06ABEH002146 https://www.mathnet.ru/eng/im/v38/i6/p1248
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Abstract page: | 479 | Russian version PDF: | 107 | English version PDF: | 9 | References: | 48 | First page: | 1 |
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