COMMUTING MAPS: A SURVEY

Commuting Dual Billiard Maps

Abstract. To a closed convex smooth curve in the plane the dual billiard transformation of its exterior corresponds: given a point outside of the curve, draw a tangent line to it through the point, and reflect the point in the point of tangency. We prove that if two curves are given, such that the corresponding dual billiard transformations commute, then the curves are concentric hornothetic el...

Canonical Metrics of Commuting Maps

Let φ : X → X be a map on an projective variety. It is known that whenever φ∗ : Pic(X) ⊗ R → Pic(X) ⊗ R has an eigenvalue α > 1, we can build a canonical measure, a canonical height and a canonical metric associated to φ. In the present work, we establish the following fact: if two commuting maps φ, ψ : X → X satisfy these conditions, for eigenvalues α and β and the same eigenvector L, then the...

A Survey of Invertibility and Spectrum Preserving Linear Maps

A COMMON FIXED POINT THEOREM FOR $psi$-WEAKLY COMMUTING MAPS IN L-FUZZY METRIC SPACES

In this paper, a common fixed point theorem for $psi$-weakly commuting maps in L-fuzzy metric spaces is proved.

Commuting maps on rank-k matrices