TY - JOUR
T1 - Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems
AU - Starkov, Konstantin E.
N1 - Funding Information:
This work was 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 - 2008/10/6
Y1 - 2008/10/6
N2 - In this Letter we study the localization problem of compact invariant sets of natural Hamiltonian systems with a polynomial Hamiltonian. Our results are based on applying the first order extremum conditions. We compute universal localizing bounds for some domain containing all compact invariant sets of a Hamiltonian system by using one quadratic function of a simple form. These bounds depend on the value of the total energy of the system, degree and some coefficients of a potential and, in addition, some positive number got as a result of a solution of one maximization problem. Besides, under some quasihomogeneity condition(s) we generalize our construction of the localization set.
AB - In this Letter we study the localization problem of compact invariant sets of natural Hamiltonian systems with a polynomial Hamiltonian. Our results are based on applying the first order extremum conditions. We compute universal localizing bounds for some domain containing all compact invariant sets of a Hamiltonian system by using one quadratic function of a simple form. These bounds depend on the value of the total energy of the system, degree and some coefficients of a potential and, in addition, some positive number got as a result of a solution of one maximization problem. Besides, under some quasihomogeneity condition(s) we generalize our construction of the localization set.
UR - http://www.scopus.com/inward/record.url?scp=51849116284&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2008.07.073
DO - 10.1016/j.physleta.2008.07.073
M3 - Artículo
SN - 0375-9601
VL - 372
SP - 6269
EP - 6272
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 41
ER -