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We consider the billiard flow of elastically colliding hard disks on the flat 2-torus and prove that no singularity manifold can locally coincide with a manifold describing future non-hyperbolicity of...
Abstract: We study a class of graph foliated spaces, or graph matchbox manifold, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity w...
Abstract: It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of poi...
Abstract: We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient co...
Abstract: Matchbox manifolds ${\mathfrak M}$ are a special class of foliated spaces, which includes as special examples the weak solenoids, and tiling spaces associated to aperiodic tilings with finit...
We study holomorphic automorphisms on compact K¨ahler manifolds having simple actions on the Hodge cohomology ring. We show for such automorphisms that the main dynamical Green currents admit complex ...

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