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Quasi-convex decomposition in o-minimal structures. Application to the gradient conjecture. (English) Zbl 1132.32004
Izumiya, Shyuichi (ed.) et al., Singularity theory and its applications. Papers from the 12th MSJ International Research Institute of the Mathematical Society of Japan, Sapporo, Japan, September 16–25, 2003. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-32-7/hbk). Advanced Studies in Pure Mathematics 43, 137-177 (2006).
In this paper the authors study the gradient conjecture of R. Thom in the o-minimal set-up.
For the entire collection see [Zbl 1110.32001].

MSC:
32B20 Semi-analytic sets, subanalytic sets, and generalizations
58K05 Critical points of functions and mappings on manifolds
37B35 Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems
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