On the quasiconformal surgery of rational functions

DOI10.24033/asens.1522zbMath0621.58030OpenAlexW172293542MaRDI QIDQ3757030

Publication date: 1987

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1987_4_20_1_1_0

zbMATH Keywords

stable region periodic point rational map Herman rings attractive basins parabolic basins nonrepelling cycles

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

Related Items

Julia sets of cubic rational maps with escaping critical points, Herman rings of elliptic functions, Lyapunov exponents, bifurcation currents and laminations in bifurcation loci, Best possibility of the Fatou-Shishikura inequality for transcendental entire functions in the Speiser class, Cubic rational maps with escaping critical points. I: Julia set dichotomy in the case of an attracting fixed point, Iteration of meromorphic functions, Quasiconformal surgery in holomorphic dynamics(Cambridge Studies in Advanced Mathematics 141)ByBodil Branner and Núria Fagella, Julia sets for the standard Newton's method, Halley's method, and Schröder's method, Perturbations of examples of Lattès and Hausdorff dimension of bifurcation place, Repelling periodic points of given periods of rational functions, On topological properties of Fatou sets and Julia sets of transcendental entire functions, Newton's method and complex dynamical systems, Rigidity of Newton dynamics, Sierpiński curve Julia sets of rational maps, Surgery on Herman rings of the standard Blaschke family, The fine structure of Herman rings, The rational maps \(F_\lambda(z)= z^m+ \lambda/z^d\) have no Herman rings, Slices of the parameter space of cubic polynomials, Bounded hyperbolic components of bicritical rational maps, A bound on the number of rationally invisible repelling orbits, A structure theorem for semi-parabolic Hénon maps, Hyperbolic components of rational maps: quantitative equidistribution and counting, On critical renormalization of complex polynomials, Rational maps without Herman rings, Dynamics of Schwarz Reflections: The Mating Phenomena, On hyperbolic rational maps with finitely connected Fatou sets, Perturbations of graphs for Newton maps I: bounded hyperbolic components, An extended Fatou-Shishikura inequality and wandering branch continua for polynomials, Boundedness of hyperbolic components of Newton maps, On the dynamics of the rational family \(f_{t}(z)={-t/4} {(z^{2}-2)^{2}/(z^{2}-1)}\), On the configuration of Herman rings of meromorphic functions, On the multipliers of repelling periodic points of entire functions, Connectivity of the Julia set for the Chebyshev-Halley family on degree \(n\) polynomials, Julia sets as buried Julia components, Hausdorff dimension of quadratic rational Julia sets, Weakly repelling fixpoints and the connectivity of wandering domains, A note on a quadratic rational map with two Siegel disks, On Rational Maps with Two Critical Points, No Herman rings for regularly ramified rational maps, A decomposition theorem for Herman maps, Attracting cycles in \(p\)-adic dynamics and height bounds for postcritically finite maps, Siegel discs, Herman rings and the Arnold family, The groupoid \(C^\ast\)-algebra of a rational map, On the connectivity of the Julia sets of meromorphic functions, On the cycles of components of disconnected Julia sets, Herman rings in the theory of iterations of endomorphisms of \(\mathbb{C}{}^*\), On the structure of Fatou domains, Examples of codification of the dynamics of arational function into a topological tree, Density of hyperbolicity for rational maps with Cantor Julia sets, A surgery on Blaschke’s function, Extensions of homeomorphisms between limbs of the Mandelbrot set, A new proof of a conjecture of Yoccoz, Iteration of functions which are meromorphic outside a small set, Connectedness of the Arnold tongues for double standard maps, On the dynamics of rational maps with two free critical points, Negativity of Lyapunov exponents and convergence of generic random polynomial dynamical systems and random relaxed Newton's methods, Structure of partially hyperbolic Hénon maps, Linearizability of saturated polynomials, Limits of rational maps, \(\mathbb{R}\)-trees and barycentric extension, Quasiconformal homeomorphisms and dynamics. III: The Teichmüller space of a holomorphic dynamical system, Fixed Point Theorems for Plane Continua with Applications, Buried Julia components and Julia sets, Herman rings with small periods and omitted values, Primitive tuning via quasiconformal surgery, Dynamics of McMullen maps, Normality and repelling periodic points, Current trends and open problems in arithmetic dynamics, On the Blaschke circle diffeomorphisms, Trees, length spectra for rational maps via barycentric extensions, and Berkovich spaces, Unbounded components in parameter space of rational maps, Singular perturbations of complex polynomials, Analytic linearization of conformal maps of the annulus, On the formulas of meromorphic functions with periodic Herman rings, Puzzles and the Fatou–Shishikura injection for rational Newton maps, Connectedness of Julia sets of rational functions, Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets, Parameter Planes for Complex Analytic Maps, DYNAMICS OF A FAMILY OF RATIONAL OPERATORS OF ARBITRARY DEGREE, Buried components of a Julia set, Density of hyperbolicity for classes of real transcendental entire functions and circle maps, Mapping the punctured plane with wandering domains, Dynamical properties of some classes of entire functions

Cites Work