On C1 classifications of hyperbolic vector fields

Some 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.

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...

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.

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...

Linearization of families of germs of hyperbolic vector fields