On \'Ecalle-Hakim's theorems in holomorphic dynamics

zbMath1359.37001arXiv1106.1710MaRDI QIDQ2948693

Marco Arizzi, Jasmin Raissy

Publication date: 6 October 2015

Full work available at URL: https://arxiv.org/abs/1106.1710

zbMATH Keywords

parabolic curvesgerms tangent to identityholomorphic dynamics in several variables

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Germs of analytic sets, local parametrization (32B10) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

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Fatou Flowers and Parabolic Curves ⋮ A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions ⋮ Stable Manifolds of Two-dimensional Biholomorphisms Asymptotic to Formal Curves ⋮ Domain of attraction for maps tangent to the identity in \(\mathbb C^2\) with characteristic direction of higher degree ⋮ Interesting examples in \(\mathbb{C}^2\) of maps tangent to the identity without domains of attraction ⋮ A note on integrability and finite orbits for subgroups of \(\mathrm{Diff}(\mathbb C^n,0)\) ⋮ Stable manifolds of biholomorphisms in Cn$\mathbb {C}^n$ asymptotic to formal curves ⋮ NOWHERE‐ANALYTIC SMOOTH CURVES WITH NON‐TRIVIAL ANALYTIC ISOTROPY ⋮ A Poincaré-Bendixson theorem for meromorphic connections on Riemann surfaces ⋮ Discrete orbits, recurrence and solvable subgroups of Diff \((\mathbb {C}^2, 0)\) ⋮ Open problems in local discrete holomorphic dynamics ⋮ Parabolic implosion for endomorphisms of \(\mathbb C^2\) ⋮ Dynamics of generic endomorphisms of Oka-Stein manifolds

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