Geometric methods in holomorphic dynamics
From MaRDI portal
Publication:6119710
DOI10.4171/icm2022/60arXiv2109.04185OpenAlexW4226032165MaRDI QIDQ6119710
Publication date: 24 March 2024
Published in: International Congress of Mathematicians (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.04185
Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Currents (32U40) Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets (37F46) Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps (37F44) Higher-dimensional holomorphic and meromorphic dynamics (37F80)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Polynomial skew-products with wandering Fatou-disks
- Classification of recurrent domains for holomorphic maps on complex projective spaces
- Semi-parabolic bifurcations in complex dimension two
- Dynamics of meromorphic mappings with small topological degree. II: Energy and invariant measure
- Polynomial diffeomorphisms of \(\mathbb{C}^ 2\). IV: The measure of maximal entropy and laminar currents
- Fatou directions along the Julia set for endomorphisms of \({\mathbb{CK}}^k\)
- Lyapunov exponents, bifurcation currents and laminations in bifurcation loci
- Distribution of postcritically finite polynomials
- Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
- Families of rational maps and iterative root-finding algorithms
- The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
- The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
- Infinitely many periodic attractors for holomorphic maps of 2 variables
- Laminar currents in \(\mathbb P^2\)
- Dynamics of rational maps: Lyapunov exponents, bifurcations, and capacity
- The intersection of laminar currents
- Entire curves and holomorphic foliations
- The dynamical Manin-Mumford problem for plane polynomial automorphisms
- Non-density of stability for holomorphic mappings on \(\mathbb{P}^k\)
- Fatou components of attracting skew-products
- Random walks, Kleinian groups, and bifurcation currents
- Classification of recurrent domains for some holomorphic maps
- Persistent nonhyperbolic transitive diffeomorphisms
- Saddle hyperbolicity implies hyperbolicity for polynomial automorphisms of \(\mathbb{C}^2\)
- A polynomial automorphism with a wandering Fatou component
- Structural instability of semi-Siegel Hénon maps
- Parabolic implosion for endomorphisms of \(\mathbb C^2\)
- Newhouse phenomenon for automorphisms of low degree in \(\mathbb{C}^3\)
- Non-wandering Fatou components for strongly attracting polynomial skew products
- Lattès maps and the interior of the bifurcation locus
- Collet, Eckmann and the bifurcation measure
- Stability and bifurcations for dissipative polynomial automorphisms of \(\mathbb C^2\)
- Hyperbolic components of rational maps: quantitative equidistribution and counting
- The supports of higher bifurcation currents
- On saddle measures
- Harmonic currents of finite energy and laminations
- Laminar currents and birational dynamics
- Classification of invariant Fatou components for dissipative Hénon maps
- Holomorphic maps on projective spaces and continuations of Fatou maps
- Sequences of multivalued meromorphic mappings and laminar currents
- A two-dimensional polynomial mapping with a wandering Fatou component
- Bifurcation currents and equidistribution on parameter space
- On stability and hyperbolicity for polynomial automorphisms of C^2
- On the dynamics of rational maps
- Distribution of rational maps with a preperiodic critical point
- Dynamics of meromorphic maps with small topological degree III: geometric currents and ergodic theory
- Polynomial Diffeomorphisms of C 2 . II: Stable Manifolds and Recurrence
- Hausdorff dimension of subsets of the parameter space for families of rational maps. (A generalization of Shishikura's result)
- Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)
- Sur la laminarité de certains courants
- Strong bifurcation loci of full Hausdorff dimension
- Parametric Lyapunov exponents
- AUTOMORPHISMS AND DYNAMICS: A LIST OF OPEN PROBLEMS
- PLURIPOTENTIAL THEORY AND COMPLEX DYNAMICS IN HIGHER DIMENSION
- Bifurcations in the elementary Desboves family
- Self-intersection of foliation cycles on complex manifolds
- Some aspects of explicit birational geometry inspired by complex dynamics
- Bifurcation currents in holomorphic dynamics on
- Un critère de laminarité locale en dimension quelconque
- Harmonic measure and expansion on the boundary of the connectedness locus.
- Dynamics of rational maps: A current on the bifurcation locus
- Dynamics of automorphisms of \(K3\) surfaces
- Wandering domains arising from Lavaurs maps with Siegel disks