| Title:
|
Calculus of flows on convenient manifolds (English) |
| Author:
|
Zajtz, Andrzej |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
355-372 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The study of diffeomorphism group actions requires methods of infinite dimensional analysis. Really convenient tools can be found in the Frölicher - Kriegl - Michor differentiation theory and its geometrical aspects. In terms of it we develop the calculus of various types of one parameter diffeomorphism groups in infinite dimensional spaces with smooth structure. Some spectral properties of the derivative of exponential mapping for manifolds are given. (English) |
| Keyword:
|
flow |
| Keyword:
|
diffeomorphism group |
| Keyword:
|
regular Lie group action |
| Keyword:
|
Frölicher-Kriegl differential calculus |
| Keyword:
|
1-parameter group of bounded operators |
| MSC:
|
22E65 |
| MSC:
|
58B25 |
| MSC:
|
58D05 |
| idZBL:
|
Zbl 0881.58012 |
| idMR:
|
MR1441405 |
| . |
| Date available:
|
2008-06-06T21:31:52Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107587 |
| . |
| Reference:
|
[1] Frölicher A., Kriegl A.: Linear spaces and differentiation theory.Pure and Applied Mathematics, J. Wiley, Chichester, 1988. Zbl 0657.46034, MR 0961256 |
| Reference:
|
[2] Grabowski J.: Free subgroups of diffeomorphism groups.Fundamenta Math. 131(1988), 103-121. Zbl 0666.58011, MR 0974661 |
| Reference:
|
[3] Grabowski J.: Derivative of the exponential mapping for infinite dimensional Lie groups.Annals Global Anal. Geom. 11(1993), 213-220. Zbl 0836.22028, MR 1237454 |
| Reference:
|
[4] Hamilton R. S.: The inverse function theorem of Nash and Moser.Bull. Amer. Math. Soc. 7(1982), 65-222. Zbl 0499.58003, MR 0656198 |
| Reference:
|
[5] Kolář I., Michor P., Slovák J.: Natural operations in differential geometry.Springer-Verlag, Berlin, Heidelberg, New York, 1993. Zbl 0782.53013, MR 1202431 |
| Reference:
|
[6] Kriegl A., Michor P.: Regular infinite dimensional Lie groups.to appear, J. of Lie Theory, 37. Zbl 0893.22012, MR 1450745 |
| Reference:
|
[7] Mather J.: Characterization of Anosov diffeomorphisms.Ind.Math., vol. 30, 5(1968), 473-483. Zbl 0165.57001, MR 0248879 |
| Reference:
|
[8] Omori H., Maeda Y., Yoshioka A.: On regular Fréchet Lie groups IV. Definitions and fundamental theorems.Tokyo J. Math. 5(1982), 365-398. MR 0688131 |
| Reference:
|
[9] Pazy A.: Semigroups of linear operators and applications to Partial Differential Equations.Springer-Verlag New York, 1983. Zbl 0516.47023, MR 0710486 |
| . |
