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A generic classification of function germs with respect to the reticular \(t-{\mathcal P}-{\mathcal K}\)-equivalence. (English) Zbl 1183.26002
By extending a notion by S. Izumiya [J. Differ. Geom. 38, No. 3, 485–500 (1993; Zbl 0781.57016)], the author introduces a general equivalence relation called “reticular \(t\)-\({\mathcal P}\)-\({\mathcal K}\)-equivalence” of function germs in \({\mathfrak M}(r; k+ n+ m)\) and gives a generic classification in the case \(r= 0\), \(n\leq 5\), \(m\leq 1\) and \(r= 1\), \(n\leq 3\), \(m\leq 1\), respectively. As it is expected, this work will play an important role in a generic classification of bifurcations of wave fronts generaetd by a hypersurface germ with a boundary (T. Tsukuda, in preparation).
MSC:
26A21 Classification of real functions; Baire classification of sets and functions
32S05 Local complex singularities
37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
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