Lower bounds for non-archimedean lyapunov exponents

Kenneth Jacobs*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let K be a complete, algebraically closed, non-Archimedean valued field, and let P 1 denote the Berkovich projective line over K. The Lyapunov exponent for a rational map Φ ε K(z) of degree d ≥ 2 measures the exponential rate of growth along a typical orbit of Φ. When Φ is defined over C, the Lyapunov exponent is bounded below by 1/2 log d. In this article, we give a lower bound for L(Φ) for maps Φ defined over non-Archimedean fields K. The bound depends only on the degree d and the Lipschitz constant of Φ. For maps Φ whose Julia sets satisfy a certain boundedness condition, we are able to remove the dependence on the Lipschitz constant.

Original languageEnglish (US)
Pages (from-to)6025-6046
Number of pages22
JournalTransactions of the American Mathematical Society
Issue number9
StatePublished - 2019


  • Distortion
  • Lower bound
  • Lyapunov exponent
  • Non-archimedean
  • Rational map

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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