We give a direct geometric proof of Hopf's theorem on the sum of indices at the zeros of a vector field in a manifold M, or rather of that part of the theorem that says that the sum is the same for ...

Analytical methods in differential systems and vector fields combine classical techniques with modern computational approaches to elucidate the intricate dynamics of nonlinear systems. Researchers use ...

In the article fine resolution of the sheaf of germs of complex projective vector fields on a locally projective complex manifold M⁴ of complex dimension n = 2 is given. The local coordinate charts on ...