Lyapunov minimizing measures for expanding maps of the circle

By G. Contreras, Artur Oscar Lopes, Ph. Thieullen. Ergodic Theory and Dynamical Systems, 2001

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ERGODIC OPTIMIZATION OF BIRKHOFF AVERAGES AND LYAPUNOV EXPONENTS (2017, unknown): “usual way), then there exists a 3 θ-Holder function hsuch that f`h˝T´hď βpfq, (1.4) Similar statements also hold for uniformly expanding maps, Anosov diﬀeomorphisms and ﬂows, etc. Some references are [27, 63, 26, 13, 48, 59, 15, 30]. The methods of proof are also diverse: some proofs use Thermodynam”
Cohomology classes of dynamically non-negative Ck functions (2002, unknown): “More direct proofs, which do not use the Ruelle transfer operator, can be found in [B1,B2, CLT ].”
Mather sets for sequences of matrices and applications to the study of joint spectral radii (2011, background): “f dμ, the set of measures which attain this average, and the set of points x ∈ X for which limn→∞ 1 n ∑n−1 i=0 f(T x) = β(f)? An overview of this research area may be found in [28]; some articles in this area of particular note include [10, 12, 15, 64].”
Ground states are generically a periodic orbit (2013, background): “[10] and it is presented in a general version in Jenkinson [15].”