Fabrizio Bianchi

activity

20232026

most citedEvery complex H{é}non map is exponentially mixing of all orders and satisfies the CLT

2 citations · 2 across the 8 of their papers we have counts for

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8 papers · 1 filter

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 $d$ holomorphic endomorphisms of $P^{2} = P^{2} (C)$ satisfying sui…

math.DS2026

Joining rigidity for rational maps

Fabrizio Bianchi, Yan Mary He

We initiate a joining rigidity theory for rational maps on the Riemann sphere $P^{1} = P^{1} (C)$ . Let $f_{1}, f_{2} : P^{1} \to P^{1}$ be rational maps of…

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

On the support of measures of large entropy for automorphisms of Kähler manifolds

Fabrizio Bianchi, Sobir Boymurodov, Karim Rakhimov

Let $f$ be a holomorphic automorphism of a compact Kähler manifold $X$ with simple action on cohomology. We show that every ergodic measure with sufficiently large entropy is suppo…

math.DS2026

Non-autonomous parabolic implosion

Matthieu Astorg, Fabrizio Bianchi

We study parabolic implosion in a general non-autonomous setting. Let $f (w) = w + w^{2} + O (w^{3})$ be a holomorphic germ tangent to the identity. We consider the iteration of non-autonomous…

math.DS2026

A Ruelle-McMullen formula for the volume dimension of skew products in $C^{2}$

Fabrizio Bianchi, Yan Mary He

Ruelle gave an explicit second-order expansion at $c = 0$ of the Hausdorff dimension of the Julia set of the quadratic family $f_{c} (z) = z^{2} + c$ . McMullen later extended this result to p…

math.DS2024

On the support of measures of large entropy for polynomial-like maps

Sardor Bazarbaev, Fabrizio Bianchi, Karim Rakhimov

Let $f$ be a polynomial-like map with dominant topological degree $d_{t} \geq 2$ and let $d_{k - 1} < d_{t}$ be its dynamical degree of order $k - 1$ . We show that the support of every ergodi…

math.DS2024

Horn maps of semi-parabolic Hénon maps

Astorg Matthieu, Bianchi Fabrizio

We prove that horn maps associated to quadratic semi-parabolic fixed points of Hénon maps, first introduced by Bedford, Smillie, and Ueda, satisfy a weak form of the Ahlfors island…

History-dependent unstable directions and the Binder--DeMarco conjecture

Joining rigidity for rational maps

A thermodynamic path metric for complex Hénon maps

On the support of measures of large entropy for automorphisms of Kähler manifolds

Non-autonomous parabolic implosion

A Ruelle-McMullen formula for the volume dimension of skew products in C2

On the support of measures of large entropy for polynomial-like maps

Horn maps of semi-parabolic Hénon maps

A Ruelle-McMullen formula for the volume dimension of skew products in $C^{2}$