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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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Quasi-Anosov diffeomorphisms and hyperbolic manifolds
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by Ricardo Mañé
Trans. Amer. Math. Soc. 229 (1977), 351-370
DOI: https://doi.org/10.1090/S0002-9947-1977-0482849-4

Abstract:

Let f be a diffeomorphism of a smooth manifold N and $M \subset N$ a compact boundaryless submanifold such that it is a hyperbolic set for f. The diffeomorphism f/M is characterized and it is proved that it is Anosov if and only if M is an invariant isolated set of f (i.e. the maximal invariant subset of some compact neighborhood). Isomorphisms of vector bundles with the property that the zero section is an isolated subset are studied proving that they can be embedded in hyperbolic vector bundle isomorphisms.
References
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Bibliographic Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 229 (1977), 351-370
  • MSC: Primary 58F15
  • DOI: https://doi.org/10.1090/S0002-9947-1977-0482849-4
  • MathSciNet review: 0482849