Hyperbolic-symmetry vector fields

Some Symmetry Classifications of Hyperbolic Vector Evolution Equations

Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations Utx = f(U,Ut, Ux) for an N -component vector U(t, x) are considered. In each class we find all scalinghomogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.

Linearization of families of germs of hyperbolic vector fields

Generic Bifurcation of Hamiltonian Vector Fields with Symmetry

One of the goals of this paper is to describe explicitly the generic movement of eigenvalues through a one-to-one resonance in a (linearized) Hamiltonian system. We classify this movement, and hence answer the question of when the collisions are “dangerous” in the sense of Krein by using a combination of group theory and definiteness properties of the associated quadratic Hamiltonian. For Resea...

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

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...