45 citations · 674 across the 102 of their papers we have counts for
10 papers · 1 filter
On the cohomology of measurable sets
Oliver Knill
If T is an ergodic automorphism of a Lebesgue probability space (X,A,m), the set of coboundries B = db =T(b)+b with symmetric difference + form a subgroup of the set of cocycles A.…
Weierstrass elliptic functions for the pendulum
Oliver Knill
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendul…
On quadratic orbital networks
Oliver Knill
These are some informal remarks on quadratic orbital networks over finite fields. We discuss connectivity, Euler characteristic, number of cliques, planarity, diameter and inductiv…
Natural orbital networks
Oliver Knill
Given a finite set T of maps on a finite ring R, we look at the finite simple graph G=(V,E) with vertex set V=R and edge set E={(a,b) | exists t in T, b=t(a), b not equal to a}. An…
Dynamically generated Networks
Oliver Knill
Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical s…
An integrable evolution equation in geometry
Oliver Knill
We introduce an integrable Hamiltonian system which Lax deforms the Dirac operator D=d+d* on a finite simple graph or compact Riemannian manifold. We show that the nonlinear isospe…