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

Alicia Cordero; José Martínez Alfaro; Pura Vindel

doi:10.3934/dcds.2008.22.587

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2008, Volume 22, Issue 3: 587-604. Doi: 10.3934/dcds.2008.22.587

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

1.
Dpt. Matemàtica Aplicada. Universidad Politécnica de Valencia, Cno. de Vera s/n. 46022 Valencia
2.
Dpt. Matemàtica Aplicada. Facultat Matemàtiques, Universitat de València. Avda. Dr. Moliner, 50, 46100 Burjassot (Valencia)
3.
Dpt. Matemàtiques. Universitat Jaume I. Campus Riu Sec., 12071 Castelló

Received: May 31, 2007

Revised: January 31, 2008

Published: August 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 37J35, 37D15; Secondary: 34C25.

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