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September  2008, 22(3): 587-604. doi: 10.3934/dcds.2008.22.587

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

Alicia Cordero 1, , José Martínez Alfaro 2, and  Pura Vindel 3,

1. 

Dpt. Matemàtica Aplicada. Universidad Politécnica de Valencia, Cno. de Vera s/n. 46022 Valencia, Spain
2. 

Dpt. Matemàtica Aplicada. Facultat Matemàtiques, Universitat de València. Avda. Dr. Moliner, 50, 46100 Burjassot (Valencia), Spain
3. 

Dpt. Matemàtiques. Universitat Jaume I. Campus Riu Sec., 12071 Castelló, Spain

Received  June 2007 Revised  February 2008 Published  August 2008

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.
Keywords: $S^{2}\times S^{1}$, Hamiltonian systems, Bott integral, round handle decomposition..
Mathematics Subject Classification: Primary: 37J35, 37D15; Secondary: 34C2.
Citation: Alicia Cordero, José Martínez Alfaro, Pura Vindel. Bott integrable Hamiltonian systems on $S^{2}\times S^{1}$. Discrete & Continuous Dynamical Systems, 2008, 22 (3) : 587-604. doi: 10.3934/dcds.2008.22.587
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