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An example of blow analytic homeomorphism. (English) Zbl 0896.58012
Fukuda, T. (ed.) et al., Real analytic and algebraic singularities. Harlow: Longman. Pitman Res. Notes Math. Ser. 381, 62-63 (1998).
The notion of a blow analytic homeomorphism introduced in [T.-C. Kuo, J. Math. Soc. Jap. 32, 605-614 (1980; Zbl 0509.58007)] and its applications to the classification theory of real analytic function-germs are discussed. In particular, the author explains that for the two blow analytic equivalent functions \(f = z(x^4+y^6)+x^6\) and \(g = z(x^4+y^6)-xy^5+x^6\) there does not exist a blow analytic homeomorphism \(h\) which is Lipschitz such that \(g = f \circ h\).
For the entire collection see [Zbl 0882.00014].

MSC:
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
32S45 Modifications; resolution of singularities (complex-analytic aspects)
58A20 Jets in global analysis
32B20 Semi-analytic sets, subanalytic sets, and generalizations
57R45 Singularities of differentiable mappings in differential topology
14P15 Real-analytic and semi-analytic sets
26E05 Real-analytic functions
26A16 Lipschitz (Hölder) classes
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