Repelling periodic points and logarithmic equidistribution in non-archimedean dynamics

Abstract

It is an open problem whether repelling periodic points are dense in the classical Julia set of a non-archimedean rational function of degree more than one. We give a partial positive answer to this question based on a study of a logarithmic equidistribution on the Berkovich projective line over non-archimedean fields.

To appear in Acta Arithmetica. For the preprint, please see <a href="http://yusuke.cajpn.org/">our home page</a>

References in corpus (1)

• Normalization of bundle holomorphic contractions and applications to dynamics

Cited by in corpus (6)

• Dynamics on Berkovich spaces in low dimensions
• Quantitative approximations of the Lyapunov exponent of a rational function over valued fields
• Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics
• Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current
• Geometric formulas on Rumely's weight function and crucial measure in non-archimedean dynamics
• Approximation of Lyapunov exponents in non-archimedean and complex dynamics