La condition de Walters

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Continuity properties of the lower spectral radius (2013, methodology): “Unlike that construction we make no use of convexity properties and do not require the preserved region C to be connected: in fact our construction more closely resembles a method used by Bousch in ergodic optimization [17, 18].”
Ergodic optimization, zero temperature limits and the max-plus algebra (2013, background): “We shall give the proof of this theorem inspired from [27].”
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”
On the Aubry–Mather theory for symbolic dynamics (2006, background): “The idea is to obtain a fixed point of a weak contraction as a limit of fixed points of strong contractions (see [3, 4]).”