Geodesic
$\mathscr{C}^{p}$-parametrization in O-minimal Structures
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 99-108

Voir la notice de l'article provenant de la source Cambridge University Press

We give a geometric and elementary proof of the uniform $\mathscr{C}^{p}$-parametrization theorem of Yomdin and Gromov in arbitrary o-minimal structures.
DOI : 10.4153/CMB-2018-030-x
Mots-clés : o-minimal structure, Cp-parametrization 
Kocel-Cynk, Beata; Pawłucki, Wiesław; Valette, Anna. $\mathscr{C}^{p}$-parametrization in O-minimal Structures. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 99-108. doi: 10.4153/CMB-2018-030-x
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[1] Burguet, D., A proof of Yomdin-Gromov’s algebraic lemma . Israel J. Math. 168(2008), 291–316. . Google Scholar | DOI

[2] Cluckers, R., Comte, G., and Loeser, F., Non-archimedean Yomdin-Gromov parametrization and points of bounded height. 2014. arxiv:1404.1952. Google Scholar

[3] Cluckers, R., Pila, J., and Wilkie, A., Uniform parametrization of subanalytic sets and diophantine applications. 2018. arxiv:1605.05916. Google Scholar

[4] Coste, M., An introduction to O-minimal geometry, Dottorato di Ricerca in Matematica, Edizioni ETS, Pisa, 2000. Google Scholar

[5] Gromov, M., Entropy, homology and semialgebraic geometry . Séminaire Bourbaki, 1985/86, Astérisque 145–146(1987), 5, 225–240. Google Scholar

[6] Hironaka, H., Introduction to real analytic sets and real analytic maps. Dottorato di Ricerca in Matematica, Edizioni ETS, Pisa, 2009. Google Scholar

[7] Kocel-Cynk, B., Pawłucki, W., and Valette, A., Short geometric proof that Hausdorff limits are definable in any o-minimal structure . Adv. Geom. 14(2014), no. 1, 49–58. . Google Scholar | DOI

[8] Kurdyka, K. and Pawłucki, W., Subanalytic version of Whitney’s extension theorem . Studia Math. 124(1997), no. 3, 269–280. Google Scholar

[9] Łojasiewicz, S., Ensembles semi-analytiques. Institut des Hautes Études Scientifiques, Bures-sur-Yvette, 1965. Google Scholar

[10] Pawłucki, W., Le théorème de Puiseux pour une application sous-analytique . Bull. Polish Acad. Sci. Math. 32(1984), no. 9–10, 555–560. Google Scholar

[11] Pawłucki, W., Lipschitz cell decomposition in o-minimal structures. I . Illinois J. Math. 52(2008), 1045–1063. Google Scholar

[12] Pila, J. and Wilkie, A. J., The rational points of a definable set . Duke Math. J. 133(2006), no. 3, 591–616. . Google Scholar | DOI

[13] Valette, G., Lipschitz triangulations . Illinois J. Math. 49(2005), no. 3, 953–979. Google Scholar

[14] Van Den Dries, L., Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series, 248, Cambridge University Press, Cambridge, 1998. . Google Scholar | DOI

[15] Yomdin, Y., Volume growth and entropy . Israel J. Math. 57(1987), 285–300. . Google Scholar | DOI

[16] Yomdin, Y., C k -resolution of semialgebraic mappings. Addendum to: “Volume growth and entropy” . Israel J. Math. 57(1987), 301–317. . Google Scholar | DOI

[17] Yomdin, Y., Analytic reparametrization of semialgebraic sets . J. Complexity 24(2008), no. 1, 54–76. . Google Scholar | DOI

[18] Yomdin, Y., Smooth parametrizations in dynamics, analysis, diophantine and computational geometry . Jpn. J. Ind. Appl. Math. 32(2015), no. 2, 411–435. . Google Scholar | DOI

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