an:06178395
Zbl 1274.34095
Hong, Chun; Zou, Lan
Abelian integrals and critical periods for a class of reversible quadratic systems
ZH
J. Sichuan Univ., Nat. Sci. Ed. 49, No. 5, 960-964 (2012).
00319575
2012
j
34C08 37J45 34C25 34C05 34C14
abelian integrals; critical periods; Picard-Fuchs equation
Summary: The authors investigate abelian integrals and critical periods of a class of reversible quadratic systems in the paper. The Picard-Fuchs equation is derived by the abelian integrals of this reversible quadratic system. Moreover, the problem of critical periods is turned into the problem of determining the number of zeros for the solution of a Riccati equation. Finally, by means of abelian integrals, conditions under which the system has an isochronous center and an increasing period function for the reversible quadratic system are given respectively.