Oberseminar "Dynamische Systeme und Kontrolltheorie" - Prof. Dr. Stefan Hilger

In the first part of my talk I will present an introduction to the Calculus on Measure Chains (Time Scales)
that was developed in my thesis 1988 (University of Würzburg).
It is possible to replace the usual time scale, the reals R underlying 1-dimensional Calculus and ODE theory by an arbitrary measure chain.
Whenever there are analogies in theories concerning discrete and continuous time scales,
this calculus is able to give a clear foundation for these analogies.
It also provides tools for tracking down reasons for discrepancies arising in theorems for different time scales.
In the second part of the talk I will give a survey about various applications of this calculus.