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A Local Hopf Bifurcation Theorem for a Certain Class of Implicit Differential Equations

Published online by Cambridge University Press:  20 November 2018

Tomasz Kaczynski  and
Wieslaw Krawcewicz
Tomasz Kaczynski
Affiliation:
Département de mathématiques et d'informatique Université de Sherbrooke Sherbrooke, Québec J1K 2R1
Wieslaw Krawcewicz
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1
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Abstract

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The local Hopf Bifurcation theorem is extended to implicit differential equations in Rn, of the form ẋ = f(x,ẋ, α), which are not solvable for the variable ẋ. The proof uses the S1 -degree of convex-valued mappings. An example of an implicit differential equation in R3 to which the presented theorem applies is provided.

Keywords

34A0934C2347H1558E09
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 2 , 01 June 1993 , pp. 183 - 189
Copyright
Copyright © Canadian Mathematical Society 1993

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