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…
Towards Adaptive Role Selection for Behavior-Based Agents
- Danny Weyns, Kurt Schelfthout, T. Holvoet, Olivier Glorieux
- Computer ScienceAdaptive Agents and Multi-Agent Systems
- 2005
Simulation results are discussed that show how the model enables the agents in the Packet-World to adapt their behavior to changes in the environment.
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…
Critical Exponent and Hausdorff Dimension in Pseudo-Riemannian Hyperbolic Geometry
- Olivier Glorieux, Daniel Monclair
- MathematicsInternational 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,…
A role based model for adaptive agents
- Danny Weyns, Kurt Schelfthout, T. Holvoet, Olivier Glorieux
- Computer Science
- 2004
Simulation results are discussed that show how the model enables the agents in the Packet-World to adapt their behavior to changes in the environment.
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…
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…
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…
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…
The embedding of the space of negatively curved surfaces in geodesic currents.
- Olivier Glorieux
- Mathematics
- 4 April 2019
We prove by an algebraic method that the embedding of the Teichmuller space in the space of geodesic currents is totally linearly independent. We prove a similar result for all negatively curved…
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