7 papers
Unstability problem of real analytic maps
Karim Bekka, Satoshi Koike, Toru Ohmoto +2
As well-known, the stability of proper maps is characterized by the infinitesimal stability. In the present paper we study the counterpart in real…
Correction to : The Kuo condition, an inequality of Thom's type and (c)-regularity
Karim Bekka, Satoshi Koike
We correct a statement of a theorem on characterisation of the (c)-regularity we gave in Topology 37 (1998), 45--62. This theorem was used in the paper in the proof of two theorems…
On the relative Kuo condition and the second relative Kuo condition
Karim Bekka, Satoshi Koike
The Kuo condition and the the second Kuo condition are known as criteria for an r-jet to be V-sufficient in C^r mappings and C^{r+1} mappings, respectively. In a previous paper we…
Equivalence of Kuo and Thom quantities for analytic functions
Karim Bekka, Satoshi Koike
Sufficiency of jets is a very important notion introduced by Rene Thom in order to establish the structural stability theory. The criteria for some sufficiency of jets are known as…
Characterisations of V-sufficiency and C^0-sufficiency of relative jets
Karim Bekka, Satoshi Koike
We consider the problems of sufficiency of jets relative to a given closed set. In the non-relative case, criteria for r-jets to be V-sufficient and C^0-sufficient in C^r mappings…
Briançon-Speder examples and the failure of weak Whitney regularity
Karim Bekka, David Trotman
It is easy to find real algebraic varieties with weakly Whitney regular stratifications which are not Whitney regular, and we give such an example in section 3 below. No examples a…