Dynamics on ℙ1: preperiodic points and pairwise stability

DOI10.1112/s0010437x23007546arXiv2212.13215MaRDI QIDQ6183955

Laura DeMarco, Niki Myrto Mavraki

Publication date: 24 January 2024

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.13215

zbMATH Keywords

bifurcationrational functionsequidistributioncurrentsheightspreperiodic points

Mathematics Subject Classification ID

Elliptic curves (14H52) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Arithmetic properties of periodic points (37P35) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rational functions with identical measure of maximal entropy
• The arithmetic Hodge index theorem for adelic line bundles
• Preperiodic points and unlikely intersections
• Bifurcations, intersections, and heights
• Iteration at the boundary of the space of rational maps
• Families of rational maps and iterative root-finding algorithms
• Dynamics of rational maps: Lyapunov exponents, bifurcations, and capacity
• Heights in families of abelian varieties and the geometric Bogomolov conjecture
• Parabolic orbifolds and the dimension of the maximal measure for rational maps
• Common preperiodic points for quadratic polynomials
• Uniformity in Mordell-Lang for curves
• Uniform Manin-Mumford for a family of genus 2 curves
• The relative Bogomolov conjecture for fibered products of elliptic curves
• Special points on fibered powers of elliptic surfaces
• On the dynamics of rational maps
• Distribution of rational maps with a preperiodic critical point
• An invariant measure for rational maps
• On the uniqueness of the maximizing measure for rational maps
• A problem of Julia sets
• When do two rational functions have the same Julia set?
• Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)
• Complex Dynamics and Renormalization (AM-135)
• Uniform Bound for the Number of Rational Points on a Pencil of Curves
• Mixed Ax–Schanuel for the universal abelian varieties and some applications
• Generic rank of Betti map and unlikely intersections
• Torsion of elliptic curves and unlikely intersections
• Bifurcation currents in holomorphic dynamics on
• Dynamics of rational maps: A current on the bifurcation locus
• Tame rational functions: decompositions of iterates and orbit intersections

This page was built for publication: Dynamics on ℙ¹: preperiodic points and pairwise stability