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28 March 2024
 
  » arxiv » 2009.13052

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Another look at the Hofer-Zehnder conjecture
Erman Cineli ; Viktor L. Ginzburg ; Basak Z. Gurel ;
Date 28 Sep 2020
AbstractWe 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.
Source arXiv, 2009.13052
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