Hilbert’s 16th problem

  Introduction the statement of Hilbert’s 16th problem: $ H(n)<\infty?$ definition of $ H(n)=max$ Limit cycle:   Try beginning with Bendixon-Poincaré theorem, which is classical stuff and belongs to a lot of textbooks on vector fields.   Affine invariance The number of limit cycle is invariant under affine map. Classification of singular point Bezout theorem Example 1.$ \frac{dx}{dt}=y,\frac{dy}{dt}=x$.The graph is just like:   2.$ \frac{dx}{dt}=x^2+y^2,\frac{dy}{dt}…