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Homoclinic tangencies, \(\Omega\)-moduli, and bifurcations. (English. Russian original) Zbl 1025.37012
Proc. Steklov Inst. Math. 236, 94-109 (2002); translation from Tr. Mat. Inst. Steklova 236, 103-119 (2002).
This paper is a survey of 16 papers of the author published during the years 1986-2000, related to the \(\Omega\)-moduli of diffeomorphisms with homoclinic tangencies and to the problem of basic bifurcations in the case of four-dimensional diffeomorphisms with a nontransversal homoclinic orbit to a fixed point of saddle-focus type \((2,2)\), i.e. to a fixed point with multipliers \(\nu_{1,2}= \lambda e^{\pm i\varphi}\) and \(\nu_{3,4}= \gamma e^{\pm i\psi}\), where \(0<\lambda <1<\gamma\) and \(\varphi,\psi \in(0,\pi)\).
For the entire collection see [Zbl 0997.00040].
Reviewer: A.Klíč (Praha)
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
37G25 Bifurcations connected with nontransversal intersection in dynamical systems
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory