8 citations · 28 across the 17 of their papers we have counts for
18 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…
Semialgebraic metric spcaes and resolution of singularities of definable sets
Masahiro Shiota
Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a defi…
Artin approximation compatible with a change of variables
Goulwen Fichou, Ronan Quarez, Masahiro Shiota
We propose a version of the classical Artin approximation which allows to perturb the variables of the approximated solution. Namely, it is possible to approximate a formal solutio…
-triangulations of semialgebraic sets
Toru Ohmoto, Masahiro Shiota
We show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is differentiable. As an application, we give a straightforward defini…
Real Milnor Fibres and Puiseux Series
Goulwen Fichou, Masahiro Shiota
Given a real polynomial function and a point in its zero locus, we defined a set consisting of algebraic real Puiseux series naturally attached to these data. We prove that this se…
Measuring definable sets in o-minimal fields
Jana Maříková, Masahiro Shiota
We introduce a non real-valued measure on the definable sets contained in the finite part of a cartesian power of an o-minimal field . The measure takes values in an ordered sem…