# 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