Integrable Systems on \(\mathbb{S}^3\). (English) Zbl 1347.37105

Summary: We classify the links of basic periodic orbits of integrable vector fields on \(\mathbb{S}^3\) generalizing results on two degree of freedom Hamiltonian systems. We also study the case of completely integrable systems and define invariants for the two classes of vector fields.


37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37D15 Morse-Smale systems
34C25 Periodic solutions to ordinary differential equations
57R30 Foliations in differential topology; geometric theory
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