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This article is cited in 7 scientific papers (total in 7 papers)
Implicit ordinary differential equations: bifurcations and sharpening of equivalence
I. A. Bogaevsky M. V. Lomonosov Moscow State University
Abstract:
We obtain a formal classification of generic local bifurcations of an implicit
ordinary differential equation at its singular points
as a single external parameter varies.
This classification consists of four normal forms,
each containing a functional invariant.
We prove that every deformation in the contact equivalence class
of an equation germ which remains quadratic in
the derivative can be obtained by a deformation of the independent
and dependent variables.
Our classification is based on a generalization of this result for families
of equations. As an application, we obtain a formal classification of generic
local bifurcations on the plane for a linear second-order partial differential
equation of mixed type at the points where the domains of ellipticity and
hyperbolicity undergo Morse bifurcations.
Keywords:
implicit ordinary differential equation, formal change of variables, normal
form, linear equation of mixed type, characteristic, bifurcation, contact
equivalence, generating function of a contact vector field.
Received: 23.12.2013
Citation:
I. A. Bogaevsky, “Implicit ordinary differential equations: bifurcations and sharpening of equivalence”, Izv. RAN. Ser. Mat., 78:6 (2014), 5–20; Izv. Math., 78:6 (2014), 1063–1078
Linking options:
https://www.mathnet.ru/eng/im8203https://doi.org/10.1070/IM2014v078n06ABEH002720 https://www.mathnet.ru/eng/im/v78/i6/p5
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Abstract page: | 758 | Russian version PDF: | 685 | English version PDF: | 33 | References: | 93 | First page: | 33 |
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