TY - JOUR
T1 - Localization of periodic orbits of polynomial vector fields of even degree by linear functions
AU - Starkov, Konstantin E.
PY - 2005/8
Y1 - 2005/8
N2 - This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered.
AB - This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered.
UR - http://www.scopus.com/inward/record.url?scp=14944364752&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2004.11.052
DO - 10.1016/j.chaos.2004.11.052
M3 - Artículo
SN - 0960-0779
VL - 25
SP - 621
EP - 627
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 3
ER -