Hyperbolic components of rational maps: quantitative equidistribution and counting
From MaRDI portal
Publication:2421727
DOI10.4171/CMH/462zbMath1431.37041arXiv1705.05276MaRDI QIDQ2421727
Thomas Gauthier, Gabriel Vigny, Yûsuke Okuyama
Publication date: 18 June 2019
Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1705.05276
Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Currents (32U40) Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets (37F46) Critical orbits for holomorphic dynamical systems (37F12)
Related Items
Parabolic bifurcation loci in the spaces of rational functions ⋮ Stability and bifurcations in projective holomorphic dynamics ⋮ Geometric methods in holomorphic dynamics ⋮ Hyperbolicity and Bifurcations in holomorphic families of polynomial skew products ⋮ DEGENERATION OF ENDOMORPHISMS OF THE COMPLEX PROJECTIVE SPACE IN THE HYBRID SPACE ⋮ Approximation of non-archimedean Lyapunov exponents and applications over global fields ⋮ The bifurcation measure has maximal entropy
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Equidistribution towards the bifurcation current. I: Multipliers and degree \(d\) polynomials
- Super-potentials of positive closed currents, intersection theory and dynamics
- Bifurcations, intersections, and heights
- Lyapunov exponents, bifurcation currents and laminations in bifurcation loci
- Distribution of postcritically finite polynomials
- Big line bundles over arithmetic varieties
- Families of rational maps and iterative root-finding algorithms
- Complex dynamics
- Dynamics of rational maps: Lyapunov exponents, bifurcations, and capacity
- Lyapunov exponent and the distribution of the periodic points of an endomorphism of \(\mathbb {CP}^k\)
- Distribution of postcritically finite polynomials. II: Speed of convergence
- The space of rational maps on \(\mathbf P^1\)
- The supports of higher bifurcation currents
- Distribution of the values of meromorphic transformations and applications
- Quantitative uniform distribution of points of small height on the projective line
- Quantitative approximations of the Lyapunov exponent of a rational function over valued fields
- Counting hyperbolic components
- Potential theory and a characterization of polynomials in complex dynamics
- Higher bifurcation currents, neutral cycles and the Mandelbrot set
- On the dynamics of rational maps
- Lyapunov Characteristic Exponents are Nonnegative
- DEGENERATION OF ENDOMORPHISMS OF THE COMPLEX PROJECTIVE SPACE IN THE HYBRID SPACE
- Distribution of rational maps with a preperiodic critical point
- Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines
- On the quasiconformal surgery of rational functions
- Sums of Lyapunov exponents for some polynomial maps of ${\bf C}^2$
- Geometry and Dynamics of Quadratic Rational Maps
- Bounded hyperbolic components of quadratic rational maps
- Distribution of postcritically finite polynomials III: Combinatorial continuity
- Quadratic polynomials, multipliers and equidistribution
- Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current
- Distribution of polynomials with cycles of a given multiplier
- Dynamics in several complex variables: endomorphisms of projective spaces and polynomial-like mapping
- Bifurcation currents in holomorphic dynamics on
- Nevanlinna theory and value distribution in the unicritical polynomials family
- Two characterizations of equilibrium measure of an endomorphism of \(P^k(\mathbb{C})\)
- Dynamics of rational maps: A current on the bifurcation locus
