Gelfreich, Vassili Exponentially small splitting of separatrices for area-preserving maps. (English) Zbl 1160.37381 Chaos Solitons Fractals 11, No. 1-3, 241-243 (2000). Summary: We discuss some recent lower and upper bounds for the splitting of separatrices for close-to-identity area-preserving maps. MSC: 37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010) 37G99 Local and nonlocal bifurcation theory for dynamical systems 37J20 Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems 70H05 Hamilton’s equations PDFBibTeX XMLCite \textit{V. Gelfreich}, Chaos Solitons Fractals 11, No. 1--3, 241--243 (2000; Zbl 1160.37381) Full Text: DOI References: [1] Fontich, E.; Simó, C., The splitting of separatrices for analytic diffeomorphisms, Ergodic Theory Dynamical Systems, 10, 295-318 (1990) · Zbl 0706.58061 [2] Gelfreich, V. G., Conjugation to a shift and the splitting of invariant manifolds, Applicationes Mathematicae, 24, 2, 127-140 (1996) · Zbl 0866.34041 [3] V.G. Gelfreich, A proof of the exponentially small transversality of the separatrices for the standard map, 1997, preprint; Comm. Math. Phys. 201 (1999) 155-219; V.G. Gelfreich, A proof of the exponentially small transversality of the separatrices for the standard map, 1997, preprint; Comm. Math. Phys. 201 (1999) 155-219 · Zbl 1042.37044 [4] Gelfreich, V. G.; Lazutkin, V. F.; Svanidze, N. V., A refined formula for the separatrix splitting for the standard map, Physica D, 71, 2, 82-101 (1994) · Zbl 0812.70017 [5] Gelfreich, V. G.; Lazutkin, V. F.; Tabanov, M. B., Exponentially small splitting in Hamiltonian systems, Chaos, 1, 2, 137-142 (1991) · Zbl 0899.58016 [6] V.F. Lazutkin, Splitting of separatrices for the Chirikov’s standard map. VINITI no. 6372/84, 1984 (Russian); V.F. Lazutkin, Splitting of separatrices for the Chirikov’s standard map. VINITI no. 6372/84, 1984 (Russian) · Zbl 1120.37039 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.