6 papers
History-dependent unstable directions and the Binder--DeMarco conjecture
Fabrizio Bianchi, Yan Mary He
We establish dimension bounds and an exact dimension formula for equilibrium measures of degree holomorphic endomorphisms of satisfying sui…
A thermodynamic path metric for complex Hénon maps
Fabrizio Bianchi, Yan Mary He
We construct a Hermitian covariance form on hyperbolic components in parameter spaces of complex Hénon maps, associated to the full complex unstable derivative cocycle. The form me…
A Ruelle-McMullen formula for the volume dimension of skew products in
Fabrizio Bianchi, Yan Mary He
Ruelle gave an explicit second-order expansion at of the Hausdorff dimension of the Julia set of the quadratic family . McMullen later extended this result to p…
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…
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…
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…