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Hausdorff dimension of limit sets for projective Anosov representations

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…
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Towards Adaptive Role Selection for Behavior-Based Agents

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.
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Critical exponent and Hausdorff dimension for quasi-Fuchsian AdS manifolds

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

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,…
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A role based model for adaptive agents

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

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

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…
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Critical exponent for geodesic currents

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…
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Regularity of limit sets of AdS quasi-Fuchsian groups

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…
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The embedding of the space of negatively curved surfaces in geodesic currents.

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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