The exponential pencil of conics

Abstract

The exponential pencil Gλ:=G1(G−10G1)λ−1, generated by two conics G0,G1, carries a rich geometric structure: It is closed under conjugation, it is compatible with duality and projective mappings, it is convergent for λ→±∞ or periodic, and it is connected in various ways with the linear pencil gλ=λG1+(1−λ)G0. The structure of the exponential pencil can be used to characterize the position of G0 and G1 relative to each other.