2 citations · 2 across the 8 of their papers we have counts for
10 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…
Joining rigidity for rational maps
Fabrizio Bianchi, Yan Mary He
We initiate a joining rigidity theory for rational maps on the Riemann sphere . Let be rational maps of…
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…
On the support of measures of large entropy for automorphisms of Kähler manifolds
Fabrizio Bianchi, Sobir Boymurodov, Karim Rakhimov
Let be a holomorphic automorphism of a compact Kähler manifold with simple action on cohomology. We show that every ergodic measure with sufficiently large entropy is suppo…
Non-autonomous parabolic implosion
Matthieu Astorg, Fabrizio Bianchi
We study parabolic implosion in a general non-autonomous setting. Let be a holomorphic germ tangent to the identity. We consider the iteration of non-autonomous…
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…
On the support of measures of large entropy for polynomial-like maps
Sardor Bazarbaev, Fabrizio Bianchi, Karim Rakhimov
Let be a polynomial-like map with dominant topological degree and let be its dynamical degree of order . We show that the support of every ergodi…
Hölder continuity and laminarity of the Green currents for Hénon-like maps
Fabrizio Bianchi, Tien-Cuong Dinh, Karim Rakhimov
Under a natural assumption on the dynamical degrees, we prove that the Green currents associated to any Hénon-like map in any dimension have Hölder continuous super-potentials, i.e…
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…
Every complex H{é}non map is exponentially mixing of all orders and satisfies the CLT
Fabrizio Bianchi, Tien-Cuong Dinh
We show that the measure of maximal entropy of every complex Hénon map is exponentially mixing of all orders for H\''older observables. As a consequence, the Central Limit Theorem…