Abstract
In this section we have three objectives: to show that
-
(1)
Infinitesimal stability is locally a condition of finite order; i.e., if the equations can be solved locally to order dim Y then they can be solved for smooth data.
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(2)
Infinitesimal stability is globally equivalent to a multijet version of local infinitesimal stability.
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(3)
Infinitesimally stable mappings form an open set.
We won’t be able to achieve our last objective just yet; but, at least, we shall be able to give a sufficient condition for the existence of a neighborhood of infinitesimally stable mappings around a given infinitesimally stable mapping.
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© 1973 Springer-Verlag New York Inc.
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Golubitsky, M., Guillemin, V. (1973). Various Equivalent Notions of Stability. In: Stable Mappings and Their Singularities. Graduate Texts in Mathematics, vol 14. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7904-5_5
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DOI: https://doi.org/10.1007/978-1-4615-7904-5_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90073-5
Online ISBN: 978-1-4615-7904-5
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