scholarly journals Resonance identity for symmetric closed characteristics on symmetric convex Hamiltonian energy hypersurfaces and its applications

2013 ◽  
Vol 255 (9) ◽  
pp. 2952-2980 ◽  
Author(s):  
Hui Liu ◽  
Yiming Long
Keyword(s):  
Symmetric Convex ◽  
Closed Characteristics ◽  
Symmetric Closed Characteristics

scholarly journals Higher P-symmetric Ekeland-Hofer capacities

2012 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kun Shi ◽  
Guangcun Lu
Keyword(s):  
Convex Bodies ◽  
Symplectic Space ◽  
Symmetric Convex ◽  
The Real ◽  
Closed Characteristics ◽  
The Relationship ◽  
Symmetric Closed Characteristics

<p style='text-indent:20px;'>This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for <inline-formula><tex-math id="M2">\begin{document}$ P $\end{document}</tex-math></inline-formula>-symmetric subsets in the standard symplectic space <inline-formula><tex-math id="M3">\begin{document}$ (\mathbb{R}^{2n},\omega_0) $\end{document}</tex-math></inline-formula>, which is motivated by Long and Dong's study about <inline-formula><tex-math id="M4">\begin{document}$ P $\end{document}</tex-math></inline-formula>-symmetric closed characteristics on <inline-formula><tex-math id="M5">\begin{document}$ P $\end{document}</tex-math></inline-formula>-symmetric convex bodies. We study the relationship between these capacities and other capacities, and give some computation examples. Moreover, we also define higher real symmetric Ekeland-Hofer capacities as a complement of Jin and the second named author's recent study of the real symmetric analogue about the first Ekeland-Hofer capacity.</p>

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