Small Dynamical Heights for Quadratic Polynomials and Rational Functions

DOI10.1080/10586458.2014.938203zbMath1347.37158arXiv1312.0491OpenAlexW1982478825MaRDI QIDQ5498931

Ruqian Chen, Robert L. Benedetto, Trevor Hyde, Yordanka Kovacheva, Colin White

Publication date: 11 February 2015

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.0491

zbMATH Keywords

heightquadratic polynomialpreperiodic pointsforward orbit

Mathematics Subject Classification ID

Heights (11G50) 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)

Related Items (3)

Bounds for preperiodic points for maps with good reduction ⋮ Current trends and open problems in arithmetic dynamics ⋮ Quadratic maps with a periodic critical point of period 2

Cites Work

• Unnamed Item
• A lower bound for average values of dynamical Green's functions
• Lower bounds on the canonical height associated to the morphism \(\phi(z)= z^d+c\)
• The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture
• Canonical heights on projective space
• Cycles of quadratic polynomials and rational points on a genus-2 curve
• The space of rational maps on \(\mathbf P^1\)
• Computing points of small height for cubic polynomials
• Periodic points on an algebraic variety
• Geometry and Dynamics of Quadratic Rational Maps

This page was built for publication: Small Dynamical Heights for Quadratic Polynomials and Rational Functions