caa a22 4500 445836628 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0764-8 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0764-8 Zaitsev Dmitri School of Mathematics, Trinity College Dublin, Dublin 2, Ireland aut Formal and finite order equivalences [Elektronische Daten] [Dmitri Zaitsev] We show that two families of germs of real-analytic subsets in $${{\mathbb C}^{n}}$$ are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of real-analytic self-maps and vector fields under conjugations. On the other hand, we provide an example of two sets of germs of smooth curves that are equivalent of any finite order but not formally equivalent. Springer-Verlag, 2010 Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 687-696 0025-5874 269:3-4<687 2011 269 209 https://doi.org/10.1007/s00209-010-0764-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0764-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zaitsev Dmitri School of Mathematics, Trinity College Dublin, Dublin 2, Ireland aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 687-696 0025-5874 269:3-4<687 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer