Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Infinitesimally stable endomorphisms
HTML articles powered by AMS MathViewer

by Hiroshi Ikeda PDF
Trans. Amer. Math. Soc. 344 (1994), 823-833 Request permission

Abstract:

It is well known that infinitesimal stability of diffeomorphisms is an open property. However, infinitesimal stability of endomorphisms is not an open property. So we consider the interior of the set of all infinitesimally stable endomorphisms. We prove that if f belongs to the interior of the set of all infinitesimally stable endomorphisms, then f is $\Omega$-stable. This means a generalization of Smale’s $\Omega$-stability theorem for diffeomorphisms. Moreover, it is proved that for Anosov endomorphisms structural stability is equivalent to lying in the interior of the set of infinitesimally stable endomorphisms.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F10, 58F15
  • Retrieve articles in all journals with MSC: 58F10, 58F15
Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 344 (1994), 823-833
  • MSC: Primary 58F10; Secondary 58F15
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1250821-2
  • MathSciNet review: 1250821