TY - JOUR
T1 - Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems
AU - Starkov, Konstantin E.
N1 - Funding Information:
This work is supported by the CONACYT project “Análisis de Localización de Conjuntos Compactos Invariantes de Sistemas no Lineales Con Dinámica Compleja y Sus Aplicaciones”, No. 000000000078890 , Mexico.
PY - 2011/8/22
Y1 - 2011/8/22
N2 - In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system.
AB - In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system.
UR - http://www.scopus.com/inward/record.url?scp=80051474208&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2011.06.064
DO - 10.1016/j.physleta.2011.06.064
M3 - Artículo
SN - 0375-9601
VL - 375
SP - 3184
EP - 3187
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 36
ER -