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A construction of realizations of perturbations of Poincaré maps. (English) Zbl 0604.58037
The author constructs a \(C^ r\)-vector field, the flow of which generates a \(C^ r\)-perturbation of a given \(C^ r\)-Poincaré map by the first intersections of its trajectories with a given transversal. The proof of this result appearing in the author’s paper [Czechosl. Math. J. 26(101), 71-83 (1976; Zbl 0342.58022)] was not quite correct. In the present paper he corrects the proof by using a special surjective mapping theorem for smooth maps.
Reviewer: Yu.Kifer

MSC:
37G99 Local and nonlocal bifurcation theory for dynamical systems
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
Citations:
Zbl 0342.58022
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References:
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