On the group of real analytic diffeomorphisms of a compact real analytic manifold
Author:
J. Leslie
Journal:
Trans. Amer. Math. Soc. 274 (1982), 651-669
MSC:
Primary 58B12; Secondary 58D05, 58F99
DOI:
https://doi.org/10.1090/S0002-9947-1982-0675073-5
MathSciNet review:
675073
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we exhibit a Lie group structure on the group of real analytic diffeomorphisms of a compact real analytic manifold. Further, we show that a variant of the Kupka-Smale theorem holds for the underlying topology of the above mentioned Lie group.
- [1] R. Abraham and J. Robbin, Transversal mappings and flows, Benjamin, New York, 1967. MR 0240836 (39:2181)
- [2] N. Bourbaki, Topologie générale, Chap. II, Hermann, Paris, 1967.
- [3] J. F. Colombeau, Differentiation et bornologie thèses, U.E.R. Mathématiques et Information, Université de Bordeaux, 1973. MR 0450969 (56:9259)
- [4] -, Sur quelques particularités du calcul différentiel dans les espaces vectoriels topologiques ou bornologiques, Rev. Roumaine Math. Pures Appl. 18 (1973), 3-17. MR 0361769 (50:14214)
- [5] J. Dieudonné, Denumerability conditions in convex vector spaces, Proc. Amer. Math. Soc. 8 (1957), 367-372. MR 0083687 (18:746d)
- [6] J. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977, pp. 320-333. MR 0508721 (58:22904)
- [7] P. Hartman, Ordinary differential equations, Wiley, New York, 1964. MR 0171038 (30:1270)
- [8] M. W. Hirsch and C. Pugh, Stable manifolds and hyperbolic sets, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R. I., 1970, pp. 133-163. MR 0271991 (42:6872)
- [9] H. Hogbe-Nlend, Théorie des bornologie et applications, Springer-Verlag, Berlin and New York, 1971. MR 0625157 (58:30002)
- [10] L. Van Hove, Topologie des espaces fonctionels analytiques et des groupes infinis de transformations, Acad. Roy. Belg. Bull. Cl. Sci. (5) 38 (1952). MR 0050161 (14:287b)
- [11] H. Jacobowitz, Implicit function theorems and isometric embeddings, Ann. of Math. 95 (1972), 191-225. MR 0307127 (46:6248)
- [12] J. Leslie, On a differential structure for the group of diffeomorphisms, Topology 6 (1967), 264-271. MR 0210147 (35:1041)
- [13] -, Some Frobenius theorems in global analysis, J. Differential Geom. 2 (1969), 279-297. MR 0251750 (40:4977)
- [14] D. C. Lewis, Invariant manifolds near an invariant point of unstable type, Amer. J. Math. 60 (1938), 577-589. MR 1507339
- [15] José Sebastio e Silva, Su certe classi di spazi localmente convessi imiportanti per le applicazioni, Rend. Mat. (5) 14 (1955), 338-410. MR 0070046 (16:1122c)
- [16] S. Smale, Differential equations and diffeomorphisms, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 17 (1963), 97-116. MR 0165537 (29:2818b)
- [17] -, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 0228014 (37:3598)
- [18] E. Zehnder, Generalized implicit function theorems with applications and some small divisor problems, Comm. Pure Appl. Math. 28 (1975), pp. 91-140. MR 0380867 (52:1764)
- [19] -, Moser's implicit function theorem in the framework of analytic smoothing, Math. Ann. 219 (1976), pp. 105-121. MR 0388440 (52:9276)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1982-0675073-5
Article copyright:
© Copyright 1982
American Mathematical Society