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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
##### Keywords:
Legendrian singularity; contact manifold; Mather theory
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