Two properties of volume growth entropy in Hilbert geometry

Bruno Colbois (1) , Patrick Verovic (2)

1 UNINE - Institut de Mathématiques
2 LAMA - Laboratoire de Mathématiques

The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy may vanish for a non-polygonal domain in the plane on the one hand, and that volume growth entropy is not always a limit on the other hand.

Mots clés: global Finsler geometry; convexity

Domaines: Géométrie métrique [math.MG]

Bruno Colbois, Patrick Verovic. Two properties of volume growth entropy in Hilbert geometry. 2012. ⟨hal-00711369v1⟩