Unstability problem of real analytic maps-Reference-Cited by-同舟云学术

Unstability problem of real analytic maps

Published:2024-07-22 Issue: Volume: Page:
ISSN:0024-6093
Container-title:Bulletin of the London Mathematical Society
language:en
Short-container-title:Bulletin of London Math Soc

Author:

Bekka Karim¹,Koike Satoshi²,Ohmoto Toru³^ORCID,Shiota Masahiro⁴,Tanabe Masato⁵

Affiliation:

1. Institut de recherche mathématique de Rennes Université de Rennes1 Campus Beaulieu Rennes Cedex France

2. Department of Mathematics Hyogo University of Teacher Education Kato Hyogo Japan

3. Department of Applied Mathematics Waseda University Shinjuku‐ku Tokyo Japan

4. Graduate School of Mathematics Nagoya University, Furo‐cho, Chigusa‐ku Nagoya Japan

5. Department of Mathematics Graduate School of Science Hokkaido University Sapporo Hokkaido Japan

Abstract

AbstractAs well known, the stability of proper maps is characterized by the infinitesimal stability. In the present paper, we study the counterpart in real analytic context. In particular, we show that the infinitesimal stability does not imply stability; for instance, a Whitney umbrella is not stable. A main tool for the proof is a relative version of Whitney's analytic approximation theorem that is shown by using H. Cartan's Theorems A and B.

Publisher

Wiley

Link

https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/blms.13124

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