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Trudy Mat. Inst. Steklova, 2020, Volume 310, Pages 86–106 (Mi tm4094)  

Various Equivalence Relations in Global Bifurcation Theory

N. B. Goncharuka, Yu. S. Ilyashenkobcd

a Department of Mathematical and Computational Sciences, University of Toronto Mississauga, 3359 Mississauga Rd., Mississauga, ON L5L 1C6, Canada
b National Research University Higher School of Economics, ul. Myasnitskaya 20, Moscow, 101000 Russia
c Independent University of Moscow, Bol'shoi Vlas'evskii per. 11, Moscow, 119002 Russia
d Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We discuss various definitions of equivalence for bifurcations of vector fields on the sphere and give a large number of examples (both known and new) that illustrate the advantages and disadvantages of different definitions. In addition to the classical definitions of strong and weak equivalence, we consider new notions of Sing-equivalence and moderate equivalence. These definitions seem to be more relevant to and consistent with the intuitive notion of equivalent bifurcations. They were introduced and used to describe the structural instability of some finite-parameter families of vector fields on the sphere and to study invariants of their classification.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1931
Russian Foundation for Basic Research 20-01-00420
This work was supported by the HSE Laboratory of Dynamical Systems and Applications (under grant 075-15-2019-1931 of the Ministry of Science and Higher Education of the Russian Federation) and by the Russian Foundation for Basic Research (project no. 20-01-00420).


DOI: https://doi.org/10.4213/tm4094

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 310, 78–97

Bibliographic databases:

UDC: 517.938.5
Received: December 4, 2019
Revised: December 4, 2019
Accepted: May 15, 2020

Citation: N. B. Goncharuk, Yu. S. Ilyashenko, “Various Equivalence Relations in Global Bifurcation Theory”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 86–106; Proc. Steklov Inst. Math., 310 (2020), 78–97

Citation in format AMSBIB
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\paper Various Equivalence Relations in Global Bifurcation Theory
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 310
\pages 86--106
\publ Steklov Math. Inst.
\publaddr Moscow
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