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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.

MSC:

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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