Two properties of volume growth entropy in Hilbert geometry
Bruno Colbois (UNINE), Patrick Verovic (LAMA)
TL;DR
This paper presents two examples in Hilbert geometry demonstrating that volume growth entropy can both fail to be a limit and vanish for certain non-polygonal domains, challenging previous assumptions.
Contribution
It provides the first known examples showing that volume growth entropy in Hilbert geometry is not always a limit and can be zero for non-polygonal domains.
Findings
Volume growth entropy is not always a limit.
Volume growth entropy can vanish for non-polygonal domains.
Challenges existing beliefs about entropy behavior in Hilbert geometry.
Abstract
The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may vanish for a non-polygonal domain in the plane on the other hand.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Analytic and geometric function theory