Topics from Ergodic Theory

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Stable sets and mean Li–Yorke chaos in positive entropy systems (2012, background): “Take k 1 = 0, then we ﬁnd inductively k 1 , k 2 , ··· such that for each m ≥ 2, one has It is not hard to check that (1)–(4) hold (see for example [26] or [14]).”
Spreading Properties and Complex Dynamics for Monostable Reaction–Diffusion Equations (2012, unknown): “Indeed, for large x, u0(x) = ρ(x) e −λ1x, where ρ(x) = ρ1(x) + ρ2(x) e −(λ2−λ1)x is bounded near +∞; (2)A uniformly continuous bounded function ρ is uniquely ergodic if the limit limh→+∞ h −1∫ x+h x F (τzρ)dz exists uniformly with respect to x ∈ R, where τzρ = ρ(·+ z) and F is any continuous real-va”
Variational principle for weighted topological pressure (2014, unknown): “[30]).”