Second order linear difference equations over discrete Hardy fields
We shall investigate the properties of solutions of second order linear difference equations defined over a discrete Hardy field via canonical valuations.
Skolem–Mahler–Lech type theorems and Picard–Vessiot theory
We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem–Mahler–Lech theorem to rational function coefficients. The second problem is whether or not for a given linear difference equation there exists a Picard–Vessiot extension inside the ring of sequences. The third problem is a certain special case of the dynamical Mordell–Lang conjecture. This allows us to deduce...
Strong normality and normality for difference fields.
The structure of strongly normal difference extensions.
Types of Singularity of Components of Difference Polynomials
Ueber den Ausdruck, welcher im Fall gleicher Wurzeln an die Stelle der Vandermondeschen alternirenden Function tritt.
Well-formed dynamics under quasi-static state feedback
Well-formed dynamics are a generalization of classical dynamics, to which they are equivalent by a quasi-static state feedback. In case such a dynamics is flat, i.e., equivalent by an endogenous feedback to a linear controllable dynamics, there exists a Brunovský type canonical form with respect to a quasi-static state feedback.