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

Zbl 0509.58007