Lower bounds for non-Archimedean Lyapunov exponents
Author:
Kenneth Jacobs
Journal:
Trans. Amer. Math. Soc. 371 (2019), 6025-6046
MSC (2010):
Primary 37P50, 11S82; Secondary 37P05
DOI:
https://doi.org/10.1090/tran/7344
Published electronically:
February 1, 2019
MathSciNet review:
3937317
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a complete, algebraically closed, non-Archimedean valued field, and let
denote the Berkovich projective line over
. The Lyapunov exponent for a rational map
of degree
measures the exponential rate of growth along a typical orbit of
. When
is defined over
, the Lyapunov exponent is bounded below by
. In this article, we give a lower bound for
for maps
defined over non-Archimedean fields
. The bound depends only on the degree
and the Lipschitz constant of
. For maps
whose Julia sets satisfy a certain boundedness condition, we are able to remove the dependence on the Lipschitz constant.
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Additional Information
Kenneth Jacobs
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email:
kjacobs@math.northwestern.edu
DOI:
https://doi.org/10.1090/tran/7344
Keywords:
Lyapunov exponent,
non-Archimedean,
rational map,
lower bound,
distortion
Received by editor(s):
October 18, 2016
Received by editor(s) in revised form:
March 6, 2017, and May 10, 2017
Published electronically:
February 1, 2019
Additional Notes:
The author gratefully acknowledges support from NSF grant DMS-1344994 of the RTG in Algebra, Algebraic Geometry, and Number Theory, at the University of Georgia.
Article copyright:
© Copyright 2019
American Mathematical Society