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

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The infinitesimal stability of semigroups of expanding maps
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by Richard Sacksteder PDF
Trans. Amer. Math. Soc. 221 (1976), 281-288 Request permission

Abstract:

The concept of ${C^\infty }$ infinitesimal stability for representations of a semigroup by ${C^\infty }$ maps is defined. In the case of expanding linear maps of the torus ${T^d}$ it is shown that certain algebraic conditions assure such stability.
References
  • M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics, Vol. 14, Springer-Verlag, New York-Heidelberg, 1973. MR 0341518
  • John N. Mather, Stability of $C^{\infty }$ mappings. II. Infinitesimal stability implies stability, Ann. of Math. (2) 89 (1969), 254–291. MR 259953, DOI 10.2307/1970668
  • Jürgen Moser, A rapidly convergent iteration method and non-linear differential equations. II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 20 (1966), 499–535. MR 206461
  • Richard Sacksteder, Abelian semi-groups of expanding maps, Recent advances in topological dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Lecture Notes in Math., Vol. 318, Springer, Berlin, 1973, pp. 235–248. MR 0423419
  • Michael Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175–199. MR 240824, DOI 10.2307/2373276
  • S. Sternberg, Celestial mechanics. Part II, Benjamin, New York, 1969.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 221 (1976), 281-288
  • MSC: Primary 58F15; Secondary 58F10
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0418166-7
  • MathSciNet review: 0418166