We consider the action of the semigroup of $n\times n$ integral matrices with positive determinant, on the space of $p$-tuples of $n$-vectors, where $p<n$. Then the orbit of a $p$-tuple is dense whenever the coordinates are not all contained in a proper rational subspace. We discuss the aspects of effectiveness of approaching a general target point, in terms of the sizes of the matrices involved. The critical exponents of the behaviour will be discussed.
Dynamics of nonsingular integral transformations and Diophantine approximation
13.07.2023 15:00 - 17:00
Organiser:
H. Bruin, R. Zweimüller
Location: