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math.DS2026
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…
math.DS2026
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…
math.DS2026
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…