Blow-analytic equivalence versus contact bi-Lipschitz equivalence

Invariants of Bi-lipschitz Equivalence of Real Analytic Functions

We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (Rn,0) → (R,0) that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admit continuous moduli. For a germ f the invariant is given in terms of the leading coefficients of the asymptotic expansions of f along the sets where the size of |x||grad...

Motivic-type Invariants of Blow-analytic Equivalence

To a given analytic function germ f : (R, 0) → (R, 0), we associate zeta functions Zf,+, Zf,− ∈ Z[[T ]], defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence ...

Blow-analytic Equivalence of Two Variable Real Analytic Function Germs

Blow-analytic equivalence is a notion for real analytic function germs, introduced by Tzee-Char Kuo in order to develop the real analytic equisingularity theory. In this paper we give several complete characterisations of blow-analytic equivalence in the two dimensional case in terms of the minimal resolutions, the real tree model for the arrangement of Newton-Puiseux roots, and the cascade blo...

Analytic equivalence relations and bi-embeddability

Complete Analytic Equivalence Relations

We prove that various concrete analytic equivalence relations arising in model theory or analysis are complete, i.e. maximum in the Borel reducibility ordering. The proofs use some general results concerning the wider class of analytic quasi-orders.