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\(C^ k\)-resolution of semialgebraic mappings, addendum to volume growth and entropy. (English) Zbl 0641.54037
[See also the preceding review.]
In this addendum the inequality (*) is proved with \(\ell /k\) instead of \(2\ell /k\) and examples are given to show that this improved inequality is sharp. From these results, it is then shown that for \(C^{\infty}\)- smooth maps \(v(f)=h(f)\).
Reviewer: D.Hurley

MSC:
54H20 Topological dynamics (MSC2010)
54C70 Entropy in general topology
37A99 Ergodic theory
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[1] M. Coste,Ensembles semi-algébriques, Lecture Notes in Math.959, Springer-Verlag, Berlin, 1982, pp. 109–138.
[2] M. Gromov,Entropy, homology and semialgebraic geometry (after Y. Yomdin), Seminaire N. Bourbaki, Volume 1985–86, Exposé 663.
[3] Y. Yomdin,Volume growth and entropy, Isr. J. Math.57 (1987), 285–300 (this issue). · Zbl 0641.54036
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