Numerical ranges, Poncelet curves, invariant measures (Q5935580)

Convex closed curves of the plane are called circuits in this paper. NEWLINENEWLINENEWLINEThe authors generalize the well-known result of Poncelet for circles and ellipses in the following sense: A circuit \(K\) is called a Poncelet curve of rank \(N\) w.r.t. a circuit \(C\), if for any point \(z \in C\) there exists a closed \(N\)-sided polygon \(P\) with vertices on \(C\) (starting vertex \(z\)), which is circumscribed by \(K\). Examples of such Poncelet curves can be generated by the use of certain square matrices \(T\). Properties of \(T\) are presented in order to gain results on the characterisation of the classical case (circle and ellipse).