2013/10/17 by Virginia Agostiniani, Agostiniani, Virginia, Riccarda Rossi +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Differential Equations Analysis #math.AP
paper · pdf · doi:10.48550/arxiv.1310.4846
arxiv created 2013/10/17 · openalex publication_date 2013/10/17 · arxiv updated 2013/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we review some results on the transversality conditions for a smooth Fredholm map f: 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∈ (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× (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.