Invariants of bi-Lipschitz equivalence of real analytic functions

Jean-Pierre Henry, and Adam Parusiński. "Invariants of bi-Lipschitz equivalence of real analytic functions." Banach Center Publications 65.1 (2004): 67-75. <http://eudml.org/doc/282431>.

@article{Jean2004,
abstract = {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 admits 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 f(x)| is comparable to the size of |f(x)|.},
author = {Jean-Pierre Henry, Adam Parusiński},
journal = {Banach Center Publications},
keywords = {real analytic function; bi-Lipschitz equivalence},
language = {eng},
number = {1},
pages = {67-75},
title = {Invariants of bi-Lipschitz equivalence of real analytic functions},
url = {http://eudml.org/doc/282431},
volume = {65},
year = {2004},
}

TY - JOUR
AU - Jean-Pierre Henry
AU - Adam Parusiński
TI - Invariants of bi-Lipschitz equivalence of real analytic functions
JO - Banach Center Publications
PY - 2004
VL - 65
IS - 1
SP - 67
EP - 75
AB - 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 admits 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 f(x)| is comparable to the size of |f(x)|.
LA - eng
KW - real analytic function; bi-Lipschitz equivalence
UR - http://eudml.org/doc/282431
ER -