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.
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