1 citations · 3 across the 12 of their papers we have counts for
14 papers
Parabolic implosion in dimension 2
Matthieu Astorg, Lorena López-Hernanz, Jasmin Raissy
In this paper, we extend the theory of parabolic implosion in complex dimension 2 to the case of holomorphic maps tangent to the identity at order 2. We investigate the bifurcation…
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…
Cubic Siegel polynomials and the bifurcation measure
Matthieu Astorg, Davoud Cheraghi, Arnaud Chéritat
We prove that cubic polynomial maps with a fixed Siegel disk and a critical orbit eventually landing inside that Siegel disk lie in the support of the bifurcation measure. This ans…
Bifurcation for families of Ahlfors island maps
Matthieu Astorg, Anna Miriam Benini, Nuria Fagella
We extend Mañé-Sad-Sullivan and Lyubich's equivalent characterization of stability to the setting of Ahlfors island maps, which include notably all meromorphic maps. As a consequen…
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…
Dynamics of skew-products tangent to the identity
Matthieu Astorg, Luka Boc Thaler
We study the local dynamics of generic skew-products tangent to the identity, i.e. maps of the form with . More precisely, we focus on map…
Bifurcation loci of families of finite type meromorphic maps
Matthieu Astorg, Anna Miriam Benini, Núria Fagella
We show that stability is open and dense in natural families of meromorphic maps of one complex variable with a finite number of singular values, and even more generally, to f…
Higher bifurcations for polynomial skew-products
Matthieu Astorg, Fabrizio Bianchi
We continue our investigation of the parameter space of families of polynomial skew products. Assuming that the base polynomial has a Julia set not totally disconnected and is neit…
Hyperbolicity and bifurcations in holomorphic families of polynomial skew products
Matthieu Astorg, Fabrizio Bianchi
We initiate a parametric study of holomorphic families of polynomial skew products, i.e., polynomial endomorphisms of of the form that exten…
Collet, Eckmann and the bifurcation measure
Matthieu Astorg, Thomas Gauthier, Nicolae Mihalache +1
The moduli space of degree rational maps can naturally be endowed with a measure detecting maximal bifurcations, called the bifurcation me…
Dynamics of post-critically finite maps in higher dimension
Matthieu Astorg
We study the dynamics of post-critically finite endomorphisms of P^k(C). We prove that post-critically finite endomorphisms are always post-critically finite all the way down under…
Summability Condition and Rigidity for Finite Type Maps
Matthieu Astorg
We extend a series of results due to Makienko, Dominguez and Sienra on the rigidity of some holomorphic dynamical systems with summable critical values to the setting of finite typ…
A two-dimensional polynomial mapping with a wandering Fatou component
Matthieu Astorg, Xavier Buff, Romain Dujardin +2
We show that there exist polynomial endomorphisms of C^2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorph…
On the dynamical Teichmüller space
Matthieu Astorg
We prove that the dynamical Teichmüller space of a rational map immerses into the space of rational maps of the same degree, answering a question of McMullen and Sullivan. This is…