A proof of Yomdin-Gromov’s Algebraic Lemma
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Following the analysis of differentiable mappings of Y. Yomdin, M. Gromov has stated a very elegant “Algebraic Lemma” which says that the “differentiable size” of an algebraic subset may be bounded only in terms of its dimension, degree and diameter, regardless of the size and specific values of the underlying coefficients. We give a complete and elementary proof of Gromov’s result.
KeywordsGroup Theory Differentiable Mapping Elementary Proof Algebraic Subset Algebraic Lemma
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- R. Benedetti and J.-L. Riesler, Real Algebraic Geometry and Semi-Algebraic Sets, Hermann, Paris, 1990.Google Scholar
- J. Buzzi, Ergodic and topological complexity of dynamical systems, Course given during the Research trimester Dynamical Systems, 2002, Pise.Google Scholar
- J. Bochnak, M. Coste and M. F. Roy, Géométrie algébrique réelle, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3 Folge, Band 12, Springer-Verlag, Berlin, Heidelberg, and New York, 1987.Google Scholar
- G. Comte and Y. Yomdin, Tame Geometry with applications in smooth Analysis, Lecture Notes in Mathematics 1834, Springer-Verlag, Berlin, 2004.Google Scholar
- T. Downarowicz, S. Newhouse, Symbolic extensions and smooth dynamical systems Inventiones Mathematicae (2004), (on line).Google Scholar