Stability in Darboux’s Theorem

1994 ◽  
pp. 336-355
Author(s):  
Yu. G. Reshetnyak
Keyword(s):  
Darboux's Theorem

A Proof of Darboux's Theorem

2010 ◽  
Vol 117 (2) ◽  
pp. 174 ◽  
Author(s):  
Sam B. Nadler, Jr.
Keyword(s):  
Darboux's Theorem

Some observations on Darboux's theorem, isospectral Hamiltonians and supersymmetry

1995 ◽  
Vol 28 (12) ◽  
pp. 3525-3532 ◽  
Author(s):  
N Nag ◽  
R Roychoudhury
Keyword(s):  
Darboux's Theorem

scholarly journals Symplectic $ {\mathbb Z}_2^n $-manifolds

2021 ◽  
Vol 13 (3) ◽  
pp. 285
Author(s):  
Andrew James Bruce ◽  
Janusz Grabowski
Keyword(s):  
Scalar Product ◽  
Symplectic Geometry ◽  
Darboux's Theorem

<p style='text-indent:20px;'>Roughly speaking, <inline-formula><tex-math id="M1">\begin{document}$ {\mathbb Z}_2^n $\end{document}</tex-math></inline-formula>-manifolds are 'manifolds' equipped with <inline-formula><tex-math id="M2">\begin{document}$ {\mathbb Z}_2^n $\end{document}</tex-math></inline-formula>-graded commutative coordinates with the sign rule being determined by the scalar product of their <inline-formula><tex-math id="M3">\begin{document}$ {\mathbb Z}_2^n $\end{document}</tex-math></inline-formula>-degrees. We examine the notion of a symplectic <inline-formula><tex-math id="M4">\begin{document}$ {\mathbb Z}_2^n $\end{document}</tex-math></inline-formula>-manifold, i.e., a <inline-formula><tex-math id="M5">\begin{document}$ {\mathbb Z}_2^n $\end{document}</tex-math></inline-formula>-manifold equipped with a symplectic two-form that may carry non-zero <inline-formula><tex-math id="M6">\begin{document}$ {\mathbb Z}_2^n $\end{document}</tex-math></inline-formula>-degree. We show that the basic notions and results of symplectic geometry generalise to the 'higher graded' setting, including a generalisation of Darboux's theorem.</p>

A New Proof of Darboux's Theorem

2004 ◽  
Vol 111 (8) ◽  
pp. 713-715 ◽  
Author(s):  
Lars Olsen
Keyword(s):  
Darboux's Theorem

Symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Lagrangian Submanifolds ◽  
Symplectic Manifolds ◽  
Contact Structures ◽  
Symplectic Topology ◽  
Symplectic Forms ◽  
The Third ◽  
Classical Construction ◽  
Darboux's Theorem

The third chapter introduces the basic notions of symplectic topology, such as symplectic forms, symplectomorphisms, and Lagrangian submanifolds. A fundamental classical construction is Moser isotopy, with its various applications such as Darboux’s theorem and the Lagrangian neighbourhood theorem. The chapter now includes a brief discussion of the Chekanov torus and Luttinger surgery. The last section on contact structures has been significantly expanded.

Darboux's Theorem and Points of Inflection

1976 ◽  
Vol 7 (3) ◽  
pp. 5 ◽  
Author(s):  
Michael Olinick ◽  
Bruce B. Peterson
Keyword(s):  
Darboux's Theorem

Role of Darboux’s theorem in supersymmetric quantum mechanics

1986 ◽  
Vol 33 (2) ◽  
pp. 594-595 ◽  
Author(s):  
Pinaki Roy ◽  
Rajkumar Roychoudhury
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
Darboux's Theorem
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