Finite Decidability


We consider germs "f" of (R^n;0) in (R{;}0) that have punctual jet of order k. When this jet determines the existence of a minimum, a maximum or a saddle of "f", we say that the germ "f" is k-decidable .

We investigate conditions that assure the k-decidability of "f" and related proprieties of k-decidable germs.

Members Active in this Field (at IME-USP)


  1. Manuel Valentim de Pera Garcia - (e-mail mane@ime.usp.br)
  2. Sônia Regina Leite Garcia - ( e-mail sonia@ime.usp.br )

Publications


  1. Jet-Detectable Extrema - Angelo Barone-Netto, Proc. Am. Math. Soc. vol. 92 n. 4 (1984) pp 604-608
  2. A note on k-decidability - Manuel Valentim de Pera Garcia, X Congresso Nacional de Matemática Aplicada e Computacional, vol. 1 pp 343-345 (1988)
  3. RTMAP-9403 Finite Decidability and Polynomials - Manuel Valentim de Pera Garcia.
  4. RTMAP-9501 Local Extrema of Analytic Functions - Angelo Barone Netto, Gianluca Gorni, Gaetano Zampieri

Projects in development


  1. Find computational criteria to decide if a germ of two variables is (or not) k-decidable.
  2. The study of relations between $k$-decidability and Liapunoff stability of equilibrium points of Hamiltonian systems.


mane at ime.usp.br

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