Gibbs measures for CAT(-1) spaces - a geometric approach that survives branching
March 27, 2023 NOON PGH 646
Abstract
CAT(-1) spaces are a far-reaching generalization of Riemannian
manifolds. We discuss recent developments in the ergodic theory of
this setting. There is a natural geodesic flow to study. We construct
a Gibbs measure for any bounded Hölder potential on the space of
geodesics, and show that when it is finite it is the unique
equilibrium state for the system. Unlike previous results in this
direction in the CAT(-1) setting, our construction does not require a
condition that the potential must agree over geodesics that share a
common segment, which is a restrictive condition beyond the Riemannian
case. To fully allow branching, much of our construction takes a
"quasi" approach which allows "wiggle" by appropriate constants. This
is joint work with Caleb Dilsavor (Ohio State).
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