A geometric criterion on embedded disks along Teichmuller geodesics implies that for uniquely ergodic translation surfaces, almost every branched N-cover via a slit is uniquely ergodic.
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4 Pith papers cite this work. Polarity classification is still indexing.
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Under compact support, gap, pinching, and weak-* proximity to volume-preservation, random walks by C² diffeomorphisms on a closed manifold M admit a unique atom-free stationary measure Υ_μ of full Frostman dimension to which μ^{*n} * δ_x converges for most x.
The paper proves equidistribution of preimages of curves for generic finitely supported random walks of the Cremona group on the inverse limit of spaces of currents across models of the plane.
Existence of dynamical Green functions for random products of non-elementary loxodromic automorphisms of A²_C implies compactly supported μ-stationary measures and stiffness when the action is non-dissipative.
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Random products of birational maps: Equidistribution of preimages of curves
The paper proves equidistribution of preimages of curves for generic finitely supported random walks of the Cremona group on the inverse limit of spaces of currents across models of the plane.