A $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbb{R}^4$

Abstract

We construct a proper $C^2$-smooth function on $\mathbb{R}^4$ such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

Authors

Viktor L. Ginzburg

Department of Mathematics, University of California Santa Cruz, Santa Cruz, CA 95064, United States

Başak Gürel

Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794, United States