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We study the geometry and dynamics of discrete subgroups $Gamma$ of $PSL(3,mathbb{C})$ with an open invariant set $Omega subset PC^2$ where the action is properly discontinuous and the quotient $Omega/Gamma$ contains a connected component whicis compact. We call such groups {it quasi-cocompact}. In this case $Omega/Gamma$ is a compact complex projective orbifold and $Omega$ is a {it divisible set}. Our first theorem refines classical work by Kobayashi-Ochiai and others about complex surfaces with a projective structure: We prove that every such group is either virtually affine or complex hyperbolic. We then classify the divisible sets that appear in this way, the corresponding quasi-cocompact groups and the orbifolds $Omega/Gamma$. We also prove that excluding a few exceptional cases, the Kulkarni region of discontinuity coincides with the equicontinuity region and is the largest open invariant set where the action is properly discontinuous.
Let $ G $ be a discrete subgroup of PU(1,n). Then $ G $ acts on $mathbb {P}^n_mathbb C$ preserving the unit ball $mathbb {H}^n_mathbb {C}$, where it acts by isometries with respect to the Bergman metric. In this work we determine the equicontinuty re
In this article we study automorphisms of Toeplitz subshifts. Such groups are abelian and any finitely generated torsion subgroup is finite and cyclic. When the complexity is non superlinear, we prove that the automorphism group is, modulo a finite c
Let $M$ be a triangulable compact manifold. We prove that, among closed subgroups of $homeo_{0}(M)$ (the identity component of the group of homeomorphisms of $M$), the subgroup consisting of volume preserving elements is maximal.
We completely describe the weak closure of the powers of the Koopman operator associated to Chacons classical automorphism. We show that weak limits of these powers are the ortho-projector to constants and an explicit family of polynomials. As a cons
It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $mathbb{Z}$ [DDPM15, CK15]. In this article we extend this result to a broader class proving that the automorphism group o