Titlebook: Limit Cycles of Differential Equations; Colin Christopher,Chengzhi Li Textbook 20071st edition Birkhäuser Basel 2007 Abelian integral.Cent

不爱防注射

Darboux IntegrabilityIn this chapter, we consider one of the two main mechanisms which seem to underlie the existence of centers in polynomial vector fields. We only hint at the historical side, which is covered in detail by Schlomiuk [57].

冥想后

voluble

SymmetryIn this chapter we consider the second mechanism which gives rise to centers in polynomial systems: the existence of an algebraic symmetry.

飞来飞去真休

星球的光亮度

Monodromy of Hyperelliptic Abelian IntegralsWe want to show that in the case of Hamiltonians of the form . where .(.) is a polynomial of degree ., the existence of a tangential center implies that either . is relatively exact, or the polynomial .(.) is .. That is, it can be expressed as a polynomial of a polynomial, .(.) = .(.(.)), in a non-trivial way.

吞下

irradicable

TRAWL

entreat

Monodromybut even if we could do so, the first integral would certainly ramify as a global object. Our desire would then be to read off some important information about the system from this global ramification.

切割