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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1973 Volume 90(132), Number 1, Pages 139–156 (Mi sm3001)

This article is cited in 173 papers

On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II

N. K. Gavrilov, L. P. Shilnikov


Abstract: Dynamical systems are considered which are close to systems with a structurally unstable homoclinic curve. A definition of accessibility of a bifuration surface is given, and it is established that a bifurcation surface $H^1$ corresponding to systems with a structurally unstable homoclinic curve will be inaccessible from at least one side. Cases are singled out in which $H^1$ can be the boundary separating Morse–Smale systems from systems with a countable number of periodic motions.
Bibliography: 14 titles.

UDC: 517.9

MSC: 58F10

Received: 28.07.1972


 English version:
Mathematics of the USSR-Sbornik, 1973, 19:1, 139–156

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© Steklov Math. Inst. of RAS, 2024