arXiv subjects
Publications and source records attributed to Alexandru Zaharia.
The Lojasiewicz exponent at infinity of an entire function measures of the infimal rate of growth of its gradient. The authors compute the Lojasiewicz exponents at infinity of the 3-variable complex polynomials x - 3 x^{2n+1} y^{2q} + 2 x^{3n+1} y^{3q} + y z
Let g:X -> Y be a smooth (i.e. C^\infty differentiable) map between two smooth manifolds. In analogy with the case of complex polynomial functions, we say that y_0 in Y is a typical value of g if there exists an open neighbourhood U of y_0 in Y, such that the restriction g:g^{-1}(U) -> U is a C^\infty trivial fibration. If y_0 in Y is not a typical value of g, then y_0 is called an atypical value of g. We denote by B_g the bifurcation set of g, i.e. the set of atypical values of g. In the case of a complex polynomial function f:C^n -> C it is known that B_f is a finite set. It was previously proved that the bifurcation sets of real polynomial functions are also finite. The aim of this note is to show that the bifurcation set B_f of a smooth definable function f:R^n -> R is finite .