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Singularities and nonhyperbolic manifolds do not coincide
Semi-dispersing billiards hyperbolicity ergodicity local ergodicity invariant manifolds Chernov–Sinai Ansatz
2012/5/9
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...
Hierarchy of graph matchbox manifolds
matchbox manifold laminations ends of leaves growth of leaves theory of levels GromovHausdorff metric
2011/9/21
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...
Stable Configurations of repelling points on compact hyperbolic Manifolds
compact hyperbolic Manifolds Dynamical Systems
2011/9/20
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...
Green Currents for Meromorphic Maps of Compact Kahler Manifolds
Green Currents Meromorphic Maps Compact Kahler Manifolds
2011/9/9
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...
Voronoi tessellations for matchbox manifolds
Voronoi tessellations Delaunay triangulations almost periodic tilings laminations solenoids matchbox manifolds
2011/9/1
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...
Dynamics of automorphisms on compact Kähler manifolds
holomorphic automorphism Green current laminar current Green measure
2010/12/14
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 ...