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arXiv · 1507.03147

A Remark on Unique Ergodicity and the Contact Type Condition

Viktor L. Ginzburg·Cesar J. Niche
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Abstract

We prove that for a broad class of exact symplectic manifolds including ${\mathbb R}^{2m}$ the Hamiltonian flow on a regular compact energy level of an autonomous Hamiltonian cannot be uniquely ergodic. This is a consequence of the Weinstein conjecture and an observation that a Hamiltonian structure with non-vanishing self-linking number must have contact type. We apply these results to show that certain types of exact twisted geodesic flows cannot be uniquely ergodic.

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Viktor L. Ginzburg, Cesar J. Niche. 2015-07-11. A Remark on Unique Ergodicity and the Contact Type Condition. https://arxiv.org/abs/1507.03147

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