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arXiv · 1511.04499

Symplectic $G$-capacities and integrable systems

Alessio Figalli·Joseph Palmer·Álvaro Pelayo
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Abstract

For any Lie group $G$, we construct a $G$-equivariant analogue of symplectic capacities and give examples when $G = \mathbb{T}^k\times\mathbb{R}^{d-k}$, in which case the capacity is an invariant of integrable systems. Then we study the continuity of these capacities, using the natural topologies on the symplectic $G$-categories on which they are defined.

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Alessio Figalli, Joseph Palmer, Álvaro Pelayo. 2015-11-14. Symplectic $G$-capacities and integrable systems. https://arxiv.org/abs/1511.04499

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