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Pré-Publication, Document De Travail Année : 2012

Hamiltonian dynamics and symplectic capacities

Résumé

We show that the cylinder B^2(1) \times \mathbb{R}^{2(n-1)} embeds symplectically into the product B^{2(n-1)}(R) \times \mathbb{R}^2 for some finite R>0, which answers a question posed by H. Hofer in 1989. This implies the nonexistence of symplectic d-capacities, 1\sqrt{3}. We supply the final arguments to answer Hofer's questions. The main tool is a construction to remove singular limits of families of embeddings.

Dates et versions

hal-00743885 , version 1 (21-10-2012)

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Alvaro Pelayo, San Vu Ngoc. Hamiltonian dynamics and symplectic capacities. 2012. ⟨hal-00743885⟩
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