TY - JOUR
T1 - Unbounded dynamics and compact invariant sets of one Hamiltonian system defined by the minimally coupled field
AU - Starkov, Konstantin E.
N1 - Publisher Copyright:
© 2014 Published by Elsevier B.V.
PY - 2015
Y1 - 2015
N2 - In this paper we study some features of global dynamics for one Hamiltonian system arisen in cosmology which is formed by the minimally coupled field; this system was introduced by Maciejewski et al. in 2007. We establish that under some simple conditions imposed on parameters of this system all trajectories are unbounded in both of time directions. Further, we present other conditions for system parameters under which we localize the domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe the case when our system possesses periodic orbits which are found explicitly. In the rest of the cases we get some localization bounds for compact invariant sets.
AB - In this paper we study some features of global dynamics for one Hamiltonian system arisen in cosmology which is formed by the minimally coupled field; this system was introduced by Maciejewski et al. in 2007. We establish that under some simple conditions imposed on parameters of this system all trajectories are unbounded in both of time directions. Further, we present other conditions for system parameters under which we localize the domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe the case when our system possesses periodic orbits which are found explicitly. In the rest of the cases we get some localization bounds for compact invariant sets.
UR - http://www.scopus.com/inward/record.url?scp=85027958120&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2014.12.037
DO - 10.1016/j.physleta.2014.12.037
M3 - Artículo
SN - 0375-9601
VL - 379
SP - 1012
EP - 1016
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 14-15
ER -