Differential representations of vector fields

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...

Topological Representations of Vector Fields

This chapter gives an overview on topological methods for vector field processing. After introducing topological features for 2D and 3D vector fields, we discuss how to extract and use them as visualization tools for complex flow phenomena. We do so both for static and dynamic fields. Finally, we introduce further applications of topological methods for compressing, simplifying, comparing, and ...

Commutant Algebras in Representations of Lie Algebras of Vector Fields

In this paper, we give an explicit description of the commutant algebras for vector fields Lie algebras Wn in their representations on Wm×n, m 6 n, which arises from the tensor product Nm CoindF n, for the basis field F of characteristic 0. The result is some analogue of Weyl’s classical reciprocity.

Lie algebras Representations and Analytic Semigroups through Dual Vector Fields

Variational representations for N -cyclically monotone vector fields

Given a convex bounded domain Ω in R and an integer N ≥ 2, we associate to any jointly Nmonotone (N − 1)-tuplet (u1, u2, ..., uN−1) of vector fields from Ω into R, a Hamiltonian H on R × R...×R, that is concave in the first variable, jointly convex in the last (N − 1) variables such that for almost all x ∈ Ω, (u1(x), u2(x), ..., uN−1(x)) = ∇2,...,NH(x, x, ..., x). Moreover, H is N -sub-antisymm...