We study isochronous centers of two classes of planar systems of ordinary differential equations. For the first class which is the Lienard systems of the form x=y-F(x), y=-g(x) with a center at the origin, we prove th...We study isochronous centers of two classes of planar systems of ordinary differential equations. For the first class which is the Lienard systems of the form x=y-F(x), y=-g(x) with a center at the origin, we prove that if g is isochronous (see Definition 1.1), then the center is isochronous if and only if F≡0. For the second class which is the Hamiltonian systems of the form i=-g(y), y=f(x) with a center at the origin, we prove that if / or g is isochronous, then the center is isochronous if and only if the other is also isochronous.展开更多
文摘We study isochronous centers of two classes of planar systems of ordinary differential equations. For the first class which is the Lienard systems of the form x=y-F(x), y=-g(x) with a center at the origin, we prove that if g is isochronous (see Definition 1.1), then the center is isochronous if and only if F≡0. For the second class which is the Hamiltonian systems of the form i=-g(y), y=f(x) with a center at the origin, we prove that if / or g is isochronous, then the center is isochronous if and only if the other is also isochronous.
