Calculus of flows on convenient manifolds

Andrzej Zajtz

Archivum Mathematicum (1996)

  • Volume: 032, Issue: 4, page 355-372
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Zajtz, Andrzej. "Calculus of flows on convenient manifolds." Archivum Mathematicum 032.4 (1996): 355-372. <http://eudml.org/doc/18476>.

@article{Zajtz1996,
abstract = {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.},
author = {Zajtz, Andrzej},
journal = {Archivum Mathematicum},
keywords = {flow; diffeomorphism group; regular Lie group action; Frölicher-Kriegl differential calculus; 1-parameter group of bounded operators; differentiable manifold; group of diffeomorphisms; exponential mapping; 1-parameter system of diffeomorphisms; Frölicher-Kriegl calculus},
language = {eng},
number = {4},
pages = {355-372},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Calculus of flows on convenient manifolds},
url = {http://eudml.org/doc/18476},
volume = {032},
year = {1996},
}

TY - JOUR
AU - Zajtz, Andrzej
TI - Calculus of flows on convenient manifolds
JO - Archivum Mathematicum
PY - 1996
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 032
IS - 4
SP - 355
EP - 372
AB - 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.
LA - eng
KW - flow; diffeomorphism group; regular Lie group action; Frölicher-Kriegl differential calculus; 1-parameter group of bounded operators; differentiable manifold; group of diffeomorphisms; exponential mapping; 1-parameter system of diffeomorphisms; Frölicher-Kriegl calculus
UR - http://eudml.org/doc/18476
ER -

References

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  1. Frölicher A., Kriegl A., Linear spaces and differentiation theory, Pure and Applied Mathematics, J. Wiley, Chichester, 1988. (1988) Zbl0657.46034MR0961256
  2. Grabowski J., Free subgroups of diffeomorphism groups, Fundamenta Math. 131(1988), 103-121. (1988) Zbl0666.58011MR0974661
  3. Grabowski J., Derivative of the exponential mapping for infinite dimensional Lie groups, Annals Global Anal. Geom. 11(1993), 213-220. (1993) Zbl0836.22028MR1237454
  4. Hamilton R. S., The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. 7(1982), 65-222. (1982) Zbl0499.58003MR0656198
  5. Kolář I., Michor P., Slovák J., Natural operations in differential geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1993. (1993) Zbl0782.53013MR1202431
  6. Kriegl A., Michor P., Regular infinite dimensional Lie groups, to appear, J. of Lie Theory, 37. Zbl0893.22012MR1450745
  7. Mather J., Characterization of Anosov diffeomorphisms, Ind.Math., vol. 30, 5(1968), 473-483. (1968) Zbl0165.57001MR0248879
  8. Omori H., Maeda Y., Yoshioka A., On regular Fréchet Lie groups IV. Definitions and fundamental theorems, Tokyo J. Math. 5(1982), 365-398. (1982) Zbl0515.58004MR0688131
  9. Pazy A., Semigroups of linear operators and applications to Partial Differential Equations, Springer-Verlag New York, 1983. (1983) Zbl0516.47023MR0710486

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