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math.DS2025
Analyticity of the Hausdorff dimension and metric structures on Misiurewicz families of polynomials
Fabrizio Bianchi, Yan Mary He
Consider a holomorphic family of polynomial maps on with the property that a critical point of is persistently preperiodic to a repelling periodi…
math.DS2025
Manhattan curves in complex dynamics and asymptotic correlation of multiplier spectra
Fabrizio Bianchi, Yan Mary He
The Manhattan curve for a pair of hyperbolic structures (possibly with cusps) on a given surface is a geometric object that encodes the growth rate of lengths of closed geodesics w…
math.DS2024
Pressure path metrics on parabolic families of polynomials
Fabrizio Bianchi, Yan Mary He
Let be a subfamily of the moduli space of degree polynomials defined by a finite number of parabolic relations. Let be a bounded stable component of with the pr…