TY - JOUR
T1 - Asymptotic Development of an Integral Operator and Boundedness of the Criticality of Potential Centers
AU - Rojas, David
PY - 2019
Y1 - 2019
N2 - We study the asymptotic development at infinity of an integral operator. We use this development to give sufficient conditions to upper bound the number of critical periodic orbits that bifurcate from the outer boundary of the period function of planar potential centers. We apply the main results to two different families: the power-like potential family x¨ = x - x , p, q∈ R, p> q; and the family of dehomogenized Loud's centers.
AB - We study the asymptotic development at infinity of an integral operator. We use this development to give sufficient conditions to upper bound the number of critical periodic orbits that bifurcate from the outer boundary of the period function of planar potential centers. We apply the main results to two different families: the power-like potential family x¨ = x - x , p, q∈ R, p> q; and the family of dehomogenized Loud's centers.
KW - Center
KW - Period function
KW - Critical periodic orbit
KW - Bifurcation
KW - Criticality
UR - https://www.scopus.com/pages/publications/85064807816
U2 - 10.1007/s10884-019-09753-2
DO - 10.1007/s10884-019-09753-2
M3 - Article
SN - 1040-7294
VL - 32
SP - 665
EP - 704
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
IS - 2
ER -