# Calculus of flows on convenient manifolds

Archivum Mathematicum (1996)

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

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topZajtz, 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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- Grabowski J., Derivative of the exponential mapping for infinite dimensional Lie groups, Annals Global Anal. Geom. 11(1993), 213-220. (1993) Zbl0836.22028MR1237454
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- Kolář I., Michor P., Slovák J., Natural operations in differential geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1993. (1993) Zbl0782.53013MR1202431
- Kriegl A., Michor P., Regular infinite dimensional Lie groups, to appear, J. of Lie Theory, 37. Zbl0893.22012MR1450745
- Mather J., Characterization of Anosov diffeomorphisms, Ind.Math., vol. 30, 5(1968), 473-483. (1968) Zbl0165.57001MR0248879
- Omori H., Maeda Y., Yoshioka A., On regular Fréchet Lie groups IV. Definitions and fundamental theorems, Tokyo J. Math. 5(1982), 365-398. (1982) MR0688131
- Pazy A., Semigroups of linear operators and applications to Partial Differential Equations, Springer-Verlag New York, 1983. (1983) Zbl0516.47023MR0710486

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