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arXiv · 2009.13052

Another look at the Hofer-Zehnder conjecture

Erman Cineli·Viktor L. Ginzburg·Basak Z. Gurel
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Abstract

We give a different and simpler proof of a slightly modified (and weaker) variant of a recent theorem of Shelukhin extending Franks' "two-or-infinitely-many" theorem to Hamiltonian diffeomorphisms in higher dimensions and establishing a sufficiently general case of the Hofer-Zehnder conjecture. A few ingredients of our proof are common with Shelukhin's original argument, the key of which is Seidel's equivariant pair-of-pants product, but the new proof highlights a different aspect of the periodic orbit dynamics of Hamiltonian diffeomorphisms.

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Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel. 2020-09-28. Another look at the Hofer-Zehnder conjecture. https://arxiv.org/abs/2009.13052

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