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Thermodynamic Formalism on SRB Measures of Compact Convex Projective manifolds, Geometry and Counting
Abstract
We study the Hilbert geodesic flow on a closed convex real projective n-dimensional manifold. We use the thermodynamic formalism for this dissipative Anosov flow to obtain a geometric description of the SRB measure. We also deduce new counting properties for the induced representations of the fundamental groups in SL(n+1, R).
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BibTeX
@misc{foulon2026thermodynamic,
title = {{Thermodynamic Formalism on SRB Measures of Compact Convex Projective manifolds, Geometry and Counting}},
author = {Patrick Foulon and Inkang Kim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39454},
eprint = {2609.39454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39454},
}
RIS
TY - UNPB
TI - Thermodynamic Formalism on SRB Measures of Compact Convex Projective manifolds, Geometry and Counting
AU - Patrick Foulon
AU - Inkang Kim
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39454
UR - https://arxiv.org/abs/2609.39454
AB - We study the Hilbert geodesic flow on a closed convex real projective n-dimensional manifold. We use the thermodynamic formalism for this dissipative Anosov flow to obtain a geometric description of the SRB measure. We also deduce new counting properties for the induced representations of the fundamental groups in SL(n+1, R).
ER -