ﻻ يوجد ملخص باللغة العربية
We construct a new invariant-the trunkenness-for volume-perserving vector fields on S^3 up to volume-preserving diffeomorphism. We prove that the trunkenness is independent from the helicity and that it is the limit of a knot invariant (called the trunk) computed on long pieces of orbits.
The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $beta$ and the per
We use the theory of calibrations to write the equation of a minimal volume vector field on a given Riemann surface.
A proof is given of the vector identity proposed by Gubarev, Stodolsky and Zakarov that relates the volume integral of the square of a 3-vector field to non-local integrals of the curl and divergence of the field. The identity is applied to the case
In this paper, we focus on the construction of high order volume preserving in- tegrators for divergence-free vector fields: the monomial basis, the exponential basis and tensor product of the monomial and the exponential basis. We first prove that t
In 1985, Barnsley and Harrington defined a ``Mandelbrot Set $mathcal{M}$ for pairs of similarities --- this is the set of complex numbers $z$ with $0<|z|<1$ for which the limit set of the semigroup generated by the similarities $x mapsto zx$ and $x m