|
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
MathSciNet review:
675073
Full-text PDF Free Access
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]
Ralph
Abraham and Joel
Robbin, Transversal mappings and flows, An appendix by Al
Kelley, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0240836
(39 #2181)
- [2]
N. Bourbaki, Topologie générale, Chap. II, Hermann, Paris, 1967.
- [3]
J.
F. Colombeau, Différentiation et bornologie, U. E. R.
de Mathématiques et d’Informatique, Université de
Bordeaux I, Talence, 1973 (French). Thèse de Doctorat
d’État de l’auteur soutenue à
l’Université de Bordeaux en Mars 1973. MR 0450969
(56 #9259)
- [4]
J.
F. Colombeau, Sur quelques particularités du calcul
différentiel dans les espaces vectoriels topologiques ou
bornologiques, Rev. Roumaine Math. Pures Appl. 18
(1973), 3–17 (French). MR 0361769
(50 #14214)
- [5]
Jean
Dieudonné, Denumerability conditions in locally
convex vector spaces, Proc. Amer. Math.
Soc. 8 (1957),
367–372. MR 0083687
(18,746d), http://dx.doi.org/10.1090/S0002-9939-1957-0083687-X
- [6]
Jack
Hale, Theory of functional differential equations, 2nd ed.,
Springer-Verlag, New York-Heidelberg, 1977. Applied Mathematical Sciences,
Vol. 3. MR
0508721 (58 #22904)
- [7]
Philip
Hartman, Ordinary differential equations, John Wiley &
Sons, Inc., New York-London-Sydney, 1964. MR 0171038
(30 #1270)
- [8]
Morris
W. Hirsch and Charles
C. Pugh, Stable manifolds and hyperbolic sets, Global Analysis
(Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math.
Soc., Providence, R.I., 1970, pp. 133–163. MR 0271991
(42 #6872)
- [9]
H.
Hogbe-Nlend, Théorie des bornologies et applications,
Lecture Notes in Mathematics, Vol. 213, Springer-Verlag, Berlin-New York,
1971 (French). MR 0625157
(58 #30002)
- [10]
Léon
Van Hove, Topologie des espaces fonctionnels analytiques et des
groupes infinis de transformations, Acad. Roy. Belgique. Bull. Cl.
Sci. (5) 38 (1952), 333–351 (French). MR 0050161
(14,287b)
- [11]
Howard
Jacobowitz, Implicit function theorems and isometric
embeddings, Ann. of Math. (2) 95 (1972),
191–225. MR 0307127
(46 #6248)
- [12]
J.
A. Leslie, On a differential structure for the group of
diffeomorphisms, Topology 6 (1967), 263–271. MR 0210147
(35 #1041)
- [13]
J.
A. Leslie, Some Frobenius theorems in global analysis, J.
Differential Geometry 2 (1968), 279–297. MR 0251750
(40 #4977)
- [14]
Daniel
C. Lewis Jr., Invariant Manifolds Near an Invariant Point of
Unstable Type, Amer. J. Math. 60 (1938), no. 3,
577–587. MR
1507339, http://dx.doi.org/10.2307/2371599
- [15]
José
Sebastião e Silva, Su certe classi di spazi localmente
convessi importanti per le applicazioni, Rend. Mat. e Appl. (5)
14 (1955), 388–410 (Italian). MR 0070046
(16,1122c)
- [16]
S.
Smale, Stable manifolds for differential equations and
diffeomorphisms, Ann. Scuola Norm. Sup. Pisa (3) 17
(1963), 97–116. MR 0165537
(29 #2818b)
- [17]
S.
Smale, Differentiable dynamical
systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 0228014
(37 #3598), http://dx.doi.org/10.1090/S0002-9904-1967-11798-1
- [18]
E.
Zehnder, Generalized implicit function theorems with applications
to some small divisor problems. I, Comm. Pure Appl. Math.
28 (1975), 91–140. MR 0380867
(52 #1764)
- [19]
Eduard
Zehnder, Moser’s implicit function theorem in the framework
of analytic smoothing, Math. Ann. 219 (1976),
no. 2, 105–121. MR 0388440
(52 #9276)
- [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)
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC:
58B12,
58D05,
58F99
Retrieve articles in all journals
with MSC:
58B12,
58D05,
58F99
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1982-0675073-5
PII:
S 0002-9947(1982)0675073-5
Article copyright:
© Copyright 1982
American Mathematical Society
|
