TY - JOUR
T1 - Periodic orbits and 10 cases of unbounded dynamics for one Hamiltonian system defined by the conformally coupled field
AU - Starkov, Konstantin E.
N1 - Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
PY - 2015/7/3
Y1 - 2015/7/3
N2 - In this paper we study invariant domains with unbounded dynamics for one cosmological Hamiltonian system which is formed by the conformally coupled field; this system was introduced by Maciejewski et al. (2007). We find a few groups of conditions imposed on parameters of this system for which all trajectories are unbounded in both of time directions. Further, we present a few groups of other conditions imposed on system parameters under which we localize the invariant domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe one group of conditions when our system possesses two periodic orbits found explicitly. In some of rest cases we get localization bounds for compact invariant sets.
AB - In this paper we study invariant domains with unbounded dynamics for one cosmological Hamiltonian system which is formed by the conformally coupled field; this system was introduced by Maciejewski et al. (2007). We find a few groups of conditions imposed on parameters of this system for which all trajectories are unbounded in both of time directions. Further, we present a few groups of other conditions imposed on system parameters under which we localize the invariant domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe one group of conditions when our system possesses two periodic orbits found explicitly. In some of rest cases we get localization bounds for compact invariant sets.
UR - http://www.scopus.com/inward/record.url?scp=84940003029&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2015.03.007
DO - 10.1016/j.physleta.2015.03.007
M3 - Artículo
SN - 0375-9601
VL - 379
SP - 1337
EP - 1341
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 20-21
ER -