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Explore conformal measures and currents in holomorphic dynamics through this mathematical lecture that overviews the Patterson-Sullivan method of constructing these fundamental concepts across various branches of the field. Delve into applications for 1D rational maps and their natural extensions, complex Henon maps, and classical Kleinian groups, while examining potential extensions to higher rank actions. Learn from this comprehensive presentation delivered at the Centre International de Rencontres Mathématiques during the thematic meeting on Complex Geometry, Complex Analysis and Dynamics. Gain insights into advanced mathematical concepts that bridge complex analysis, dynamical systems, and geometric measure theory, presented by an expert in the field of holomorphic dynamics.
