Algebraic vector fields on S2

Algebraic Solutions of Plane Vector Fields

We present an algorithm that can be used to check whether a given derivation of the complex affine plane has an algebraic solution and discuss the performance of its implementation in the computer algebra system Singular.

Discrete Vector Fields and Fundamental Algebraic Topology

2 Discrete vector fields. 4 2.1 W-contractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Algebraic discrete vector fields. . . . . . . . . . . . . . . . . . . . . 6 2.3 V-paths and admissible vector fields. . . . . . . . . . . . . . . . . . 7 2.4 Reductions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.1 Definition. . . . . . . . . . . . . . . . . ...

On Algebraic Proofs of Stability for Homogeneous Vector Fields

We prove that if a homogeneous, continuously differentiable vector field is asymptotically stable, then it admits a Lyapunov function which is the ratio of two polynomials (i.e., a rational function). We further show that when the vector field is polynomial, the Lyapunov inequalities on both the rational function and its derivative have sums of squares certificates and hence such a Lyapunov fun...

Concurrent vector fields on Finsler spaces

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

On Decidable Algebraic Fields