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Towards Adaptive Role Selection for Behavior-Based Agents

- Danny Weyns, Kurt Schelfthout, T. Holvoet, Olivier Glorieux
- Computer Science
- Adaptive Agents and Multi-Agent Systems
- 2005

TLDR

Critical Exponent and Hausdorff Dimension in Pseudo-Riemannian Hyperbolic Geometry

- Olivier Glorieux, Daniel Monclair
- Mathematics
- International Mathematics Research Notices
- 17 June 2016

The aim of this article is to understand the geometry of limit sets in pseudo-Riemannian hyperbolic geometry. We focus on a class of subgroups of $\textrm{PO}(p,q+1)$ introduced by Danciger,… Expand

Regularity of limit sets of AdS quasi-Fuchsian groups

- Olivier Glorieux, Daniel Monclair
- Mathematics
- 27 September 2018

Limit sets of $\mathrm{AdS}$-quasi-Fuchsian groups of $\mathrm{PO}(n,2)$ are always Lipschitz submanifolds. The aim of this article is to show that they are never $\mathcal{C}^1$, except for the case… Expand

Critical exponent and Hausdorff dimension for quasi-Fuchsian AdS manifolds

- Olivier Glorieux, Daniel Monclair
- Mathematics
- 17 June 2016

The aim of this article is to understand the geometry of limit sets in Anti-de Sitter space. We focus on a particular type of subgroups of $\mathrm{SO}(2,n)$ called quasi-Fuchsian groups (which are… Expand

Hausdorff dimension of limit sets for projective Anosov representations

- Olivier Glorieux, Daniel Monclair, Nicolas Tholozan
- Mathematics
- 5 February 2019

We study the relation between critical exponents and Hausdorff dimensions of limit sets for projective Anosov representations. We prove that the Hausdorff dimension of the symmetric limit set in… Expand

A role based model for adaptive agents

- Danny Weyns, Kurt Schelfthout, T. Holvoet, Olivier Glorieux
- Computer Science
- 2004

TLDR

Critical exponent for geodesic currents

- Olivier Glorieux
- Mathematics
- 21 April 2017

For any geodesic current we associated a quasi-metric space. For a subclass of geodesic currents, called filling, it defines a metric and we study the critical exponent associated to this space. We… Expand

Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds

- Olivier Glorieux
- Mathematics
- 31 March 2015

We propose a definition for the length of closed geodesics in a globally hyperbolic maximal compact (GHMC) Anti-De Sitter manifold. We then prove that the number of closed geodesics of length less… Expand

Entropy of embedded surfaces in quasi-fuchsian manifolds

- Olivier Glorieux
- Mathematics
- 12 October 2015

We compare critical exponent for quasi-Fuchsian groups acting on the hyperbolic 3-space, $\mathbb{H}^3$, and on invariant disks embedded in $\mathbb{H}^3$. We give a rigidity theorem for all embedded… Expand

Critical exponent of graphed Teichmüller representations on ℍ 2 ×ℍ 2

- Olivier Glorieux
- Mathematics
- 2015

— In this note we survey different results on critical exponent. After giving the general setting and classical known results we study critical exponent associated to a pair of Teichmüller… Expand

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