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# Bott integrable Hamiltonian systems on $S^{2}\times S^{1}$

• In this paper, we study the topology of Bott integrable Hamiltonian flows on $S^{2}\times S^{1}$ in terms of some types of periodic orbits, called NMS periodic orbits. The set of these periodic orbits can be identified by means of some operations applied on global and local links. These operations come from the round handle decomposition of these systems on $S^{2}\times S^{1}.$ We apply the results to obtain a non-integrability criterium.
Mathematics Subject Classification: Primary: 37J35, 37D15; Secondary: 34C25.

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