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Numeric invariants in semilocal bifurcations

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Abstract

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.

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Acknowledgements

Both authors are partially supported by the RFBR, Grant # 20-01-00420. The second author is partially supported by Laboratory of Dynamical Systems and Applications NRU HSE, of the Ministry of science and higher education of the RF Grant ag. # 075- 15-2019-1931.

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Correspondence to Yu. Ilyashenko.

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Dukov, A., Ilyashenko, Y. Numeric invariants in semilocal bifurcations. J. Fixed Point Theory Appl. 23, 3 (2021). https://doi.org/10.1007/s11784-020-00837-x

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  • DOI: https://doi.org/10.1007/s11784-020-00837-x

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