A local variational principle for conditional entropy

By Wen Huang, Xiangdong Ye, Guohua Zhang. Ergodic Theory and Dynamical Systems, 2006

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Local entropy theory for a countable discrete amenable group action (2010, methodology): “From then on, the local entropy theory of Z -actions have been made great achievements [1, 2, 3, 4, 5, 11, 16, 21, 23, 24, 25, 27, 40, 46], see also the relevant chapters in [17] and the survey papers [19, 20].”
Unstable Entropies and Variational Principle for Partially Hyperbolic Diffeomorphisms (2017, background): “3 in [5]) 0 ≤ Hμ(α|β) − aHμ1(α|β) − (1− a)Hμ2(α|β) ≤ φ(a) + φ(1− a) where φ(x) = −x log x.”
Local Entropy Theory of a Random Dynamical System (2011, background): “1 following the ideas of [35, 37, 55, 74] and the references therein.”
Entropy points and applications (2007, background): “Moreover, a local variational principle for conditional entropy was proved [16], and relative entropy tuples in both settings, relative u.”
A local variational principle of pressure and its applications to equilibrium states (2007, background): “htop(T,U) = sup{h+ µ(T,U) : µ is a T-invariant measure} (see also [ 19 ] for a relative version).”