Dukov, A.; Ilyashenko, Yu. Numeric invariants in semilocal bifurcations. (English) Zbl 1464.37030 J. Fixed Point Theory Appl. 23, No. 1, Paper No. 3, 16 p. (2021). Summary: Bifurcations that occur in a small neighborhood of a polycycle of a planar vector field are called semilocal. We prove that even semilocal bifurcations of hyperbolic polycycles may have numeric invariants of topological classification. Cited in 1 Document MSC: 37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 37G05 Normal forms for dynamical systems 37G10 Bifurcations of singular points in dynamical systems 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 47J15 Abstract bifurcation theory involving nonlinear operators Keywords:semilocal bifurcations; hyperbolic polycycles; numeric invariants PDFBibTeX XMLCite \textit{A. Dukov} and \textit{Yu. Ilyashenko}, J. Fixed Point Theory Appl. 23, No. 1, Paper No. 3, 16 p. (2021; Zbl 1464.37030) Full Text: DOI References: [1] Arnold, V., Afraimovich, V., Ilyashenko, Yu, Shilnikov, L. (1999) Bifurcation theory and catastrophe theory. Translated from the 1986 Russian original by N. D. Kazarinoff, Reprint of the 1994 English edition from the series Encyclopaedia of Mathematical Sciences [Dynamical systems. V, Encyclopaedia Math. Sci., 5, Springer, Berlin, (1994); Springer-Verlag, Berlin, (1999). viii+271 pp · Zbl 1038.37500 [2] Goncharuk, N., Ilyashenko, Yu. Large bifurcation supports (2018). arXiv:1804.04596 [3] Goncharuk, N., Kudryashov, Yu. Bifurcations of the polycycle “tears of the heart”: multiple numerical invariants. Moscow Math J. (2018) arXiv: 1808.07459 [math.DS] (To appear) · Zbl 1465.34057 [4] Ilyashenko, Yu; Kudryashov, Yu; Schurov, I., Global bifurcations in the two-sphere: a new perspective, Invent Math, 213, 2, 461-506 (2018) · Zbl 1434.34036 · doi:10.1007/s00222-018-0793-1 [5] Sotomayor, J., Generic one-parameter families of vector fields on two-dimensional manifolds, Publ Math l’IHES, 43, 5-46 (1974) · Zbl 0279.58008 · doi:10.1007/BF02684365 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.