A \(C^2\)-smooth counterexample to the Hamiltonian Seifert conjecture in \(\mathbb R^4\). (English) Zbl 1140.37356

Ginzburg, Viktor L.; Gürel, Başak Z.

Ann. Math. (2) 158, No. 3, 953-976 (2003).

Summary: We give a detailed construction of 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.

MSC:

37J45	Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37C27	Periodic orbits of vector fields and flows
37J05	Relations of dynamical systems with symplectic geometry and topology (MSC2010)
53D35	Global theory of symplectic and contact manifolds
57R25	Vector fields, frame fields in differential topology