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EnglishIn this note we review some results on the transversality conditions for a smooth Fredholm map f : X x (0, T) -> Y between two Banach spaces X, Y. These conditions are well-known in the realm of bifurcation theory and commonly accepted as "generic". Here we show that under the transversality assumptions the sections C(t) = {x : f (x, t) = 0} of the zero set of f are discrete for every t is an element of(0, T) and we discuss a somehow explicit family of perturbations of f along which transversality holds up to a residual set. The application of these results to the case when f is the X-differential of a time-dependent energy functional E : X x (0, T) -> R and C(t) is the set of the critical points of E provides the motivation and the main example of this paper.
| Titolo: | On the transversality conditions and their genericity | |
| Autori: | Agostiniani V; Rossi R; Savaré G | |
| Rivista: | ||
| Data di pubblicazione: | 2015 | |
| Volume: | 64 | |
| Fascicolo: | 1 | |
| Pagina iniziale: | 101 | |
| Pagina finale: | 116 | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s12215-014-0184-4 | |
| URL: | https://arxiv.org/abs/1310.4846 | |
| Appare nelle tipologie: | 1.1 Journal article |
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http://hdl.handle.net/20.500.11767/33146
