Mikhail Lyubich

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math.DS2026

Equidistribution of currents under Anosov group actions

Nguyen-Bac Dang, Michael Kapovich, Mikhail Lyubich +1

We study the behavior of currents on flag-manifolds under actions of Anosov subgroups of complex semisimple Lie groups G. Given a current T of bidimension (k, k) on the full flag-m…

math.DS2025

Uniform a priori bounds for neutral renormalization. Variation II: $ψ^{∙}$ -ql Siegel maps

Dzmitry Dudko, Yusheng Luo, Mikhail Lyubich

We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to $ψ^{∙}$ -quadratic-like Siegel maps. In this form, the bounds are compatible with the $ψ$ -quadratic-l…

math.DS2025

Antiholomorphic correspondences and mating II: Shabat polynomial slices

Mikhail Lyubich, Jacob Mazor, Sabyasachi Mukherjee

We study natural one-parameter families of antiholomorphic correspondences arising from univalent restrictions of Shabat polynomials, indexed by rooted dessin d'enfants. We prove t…

Equidistribution of currents under Anosov group actions

Uniform a priori bounds for neutral renormalization. Variation II: ψ∙-ql Siegel maps

Antiholomorphic correspondences and mating II: Shabat polynomial slices

Uniform a priori bounds for neutral renormalization. Variation II: $ψ^{∙}$ -ql Siegel maps