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Higher P-symmetric Ekeland-Hofer capacities

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    *Corresponding author

Partially supported by the NNSF 11271044 of China

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  • This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for $ P $-symmetric subsets in the standard symplectic space $ (\mathbb{R}^{2n},\omega_0) $, which is motivated by Long and Dong's study about $ P $-symmetric closed characteristics on $ P $-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.

    Mathematics Subject Classification: Primary: 53D35, 53C23; Secondary: 70H05, 49J35.


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