Abstract
AbstractWe prove that if $${\varvec{\mu }}$$
μ
is a finitely supported measure on $${\varvec{SL}}_{\textbf{2}}({\mathbb {R}})$$
SL
2
(
R
)
with positive Lyapunov exponent but not uniformly hyperbolic, then the Lyapunov exponent function is not $${\varvec{\alpha }}$$
α
-Hölder around $${\varvec{\mu }}$$
μ
for any $${\varvec{\alpha }}$$
α
exceeding the Shannon entropy of $${\varvec{\mu }}$$
μ
over the Lyapunov exponent of $${\varvec{\mu }}$$
μ
.
Funder
Uniwersytet Mikolaja Kopernika w Toruniu
Fundação da Faculdade de Ciências da Universidade de Lisboa
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
2 articles.
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