Viterbo's conjecture for certain Hamiltonians in classical mechanics

Roman Karasev; Anastasia Sharipova

doi:10.1007/s40598-019-00129-4

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arXiv · 1812.03039

Viterbo's conjecture for certain Hamiltonians in classical mechanics

Roman Karasev·Anastasia Sharipova

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Abstract

We study some particular cases of Viterbo's conjecture relating volumes of convex bodies and actions of closed characteristics on their boundaries, focusing on the case of a Hamiltonian of classical mechanical type, splitting into summands depending on the coordinates and the momentum separately. We manage to establish the conjecture for sublevel sets of convex $2$-homogeneous Hamiltonians of this kind in several particular cases. We also discuss open cases of this conjecture.

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Roman Karasev, Anastasia Sharipova. 2019-12-08. Viterbo's conjecture for certain Hamiltonians in classical mechanics. https://doi.org/10.1007/s40598-019-00129-4

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