Zobrazeno 1 - 7
of 7
pro vyhledávání: '"Matthieu Astorg"'
Autor:
Matthieu, Astorg, Fabrizio, Bianchi
We prove that horn maps associated to quadratic semi-parabolic fixed points of H\'enon maps, first introduced by Bedford, Smillie, and Ueda, satisfy a weak form of the Ahlfors island property. As a consequence, two natural definitions of their Julia
Externí odkaz:
http://arxiv.org/abs/2403.20211
Publikováno v:
Analysis & PDE 16 (2023) 35-88
The classification of Fatou components for rational functions was concluded with Sullivan's proof of the No Wandering Domains Theorem in 1985. In 2016 it was shown, in joint work of the first and last author with Buff, Dujardin and Raissy, that wande
Externí odkaz:
http://arxiv.org/abs/1907.04140
Autor:
Matthieu Astorg
Publikováno v:
Ergodic Theory and Dynamical Systems. 40:289-308
We study the dynamics of post-critically finite endomorphisms of $\mathbb{P}^{k}(\mathbb{C})$. We prove that post-critically finite endomorphisms are always post-critically finite all the way down under a regularity condition on the post-critical set
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f7e943e427f8596c99b739debd439310
https://doi.org/10.1017/etds.2018.32
https://doi.org/10.1017/etds.2018.32
Autor:
Matthieu Astorg
Publikováno v:
Advances in Mathematics
Advances in Mathematics, 2017, 313, pp.991-1023. ⟨10.1016/j.aim.2017.04.013⟩
Advances in Mathematics, 2017, 313, pp.991-1023. ⟨10.1016/j.aim.2017.04.013⟩
We prove that the Teichmuller space of a rational map immerses into the moduli space of rational maps of the same degree, answering a question of McMullen and Sullivan. This is achieved through a new description of the tangent and cotangent space of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11b15c467cdfb8bff899fc925cf722e5
https://doi.org/10.1016/j.aim.2017.04.013
https://doi.org/10.1016/j.aim.2017.04.013
Publikováno v:
Inventiones Mathematicae
Inventiones Mathematicae, Springer Verlag, 2019, 217 (3), pp.749-797. ⟨10.1007/s00222-019-00874-5⟩
Inventiones Mathematicae, Springer Verlag, 2019, 217 (3), pp.749-797. ⟨10.1007/s00222-019-00874-5⟩
The moduli space $$\mathcal {M}_d$$ of degree $$d\ge 2$$ rational maps can naturally be endowed with a measure $$\mu _{\text{ bif }}$$ detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation measur
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9cbf3144f8c27fd7dfc7c15d07cdcbac
https://hal.archives-ouvertes.fr/hal-01888305
https://hal.archives-ouvertes.fr/hal-01888305
Publikováno v:
Annals of Mathematics
Annals of Mathematics, 2016, 184 (1), pp.263-313. ⟨10.4007/annals.2016.184.1.2⟩
Annals of Mathematics, Princeton University, Department of Mathematics, 2016, 184 (1), pp.263-313. ⟨10.4007/annals.2016.184.1.2⟩
Annals of Mathematics, 184(1), 263-313. Princeton University Press
Annals of Mathematics, 2016, 184 (1), pp.263-313. ⟨10.4007/annals.2016.184.1.2⟩
Annals of Mathematics, Princeton University, Department of Mathematics, 2016, 184 (1), pp.263-313. ⟨10.4007/annals.2016.184.1.2⟩
Annals of Mathematics, 184(1), 263-313. Princeton University Press
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 holomorphically of P^2(C). We also find real examples with wandering domains in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::403f5e154de7dc4263cede7e8c070e6a
https://hal.science/hal-01610414/document
https://hal.science/hal-01610414/document
Autor:
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 type maps. We also recover a shorter proof of a transversality theorem of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c3e67ee6ab1304445bd6353b02fa9ce
https://hal.archives-ouvertes.fr/hal-01275140/file/summability.pdf
https://hal.archives-ouvertes.fr/hal-01275140/file/summability.pdf