Abstract
This Chapter is technical in essence, here we present in all details two popular versions of the so-called Finite Exact Reduction, useful in many topological and geometrical questions treated in this book.
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Notes
- 1.
Some other time we will need the following basic fact: contractive perturbations of the identity in \(\mathbb{R}^{n}\) are bi-Lipschitz homeomorphisms.
- 2.
Compared with the three operations involving generating functions that left unchanged the generated Lagrangian submanifold, see Sect. 7.2.1.
References
M. Chaperon, Lois de conservation et géométrie symplectique. C. R. Acad. Sci. Paris Sér. I Math. 312(4), 345–348 (1991)
M. Chaperon, Familles génératrices. Cours l’école d’été Erasmus de Samos (Publication Erasmus de l’Université de Thessalonique, 1993)
K. Deimling, Nonlinear Functional Analysis (Springer, Berlin/New York, 1985)
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Cardin, F. (2015). Finite Exact Reductions. In: Elementary Symplectic Topology and Mechanics. Lecture Notes of the Unione Matematica Italiana, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-11026-4_8
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DOI: https://doi.org/10.1007/978-3-319-11026-4_8
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