EQUILIBRIUM STATES IN ERGODIC THEORY (London Mathematical Society Student Texts 42) By G ERHARD K ELLER : 178 pp., £16.95 (LMS members' price £12.71), ISBN 0-521-59534-7 (Cambridge University Press,…

By H. Crauel. 2001

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Square summability of variations of g-functions and uniqueness of g-measures (2003, background): “That the larger set M(T ) of T -invariant measures is generated by its minimal elements is well known: see [9].”
Higher-dimensional multifractal analysis (2002, background): “On the other hand, all β-shifts are expansive, and thus the entropy is upper semi-continuous (see [8] for details), but for β in a residual set of full Lebesgue measure the corresponding β-shift does not satisfy specification (see [11]).”
Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures (2006, background): “For example, all βshifts are expansive, and thus the entropy is upper semi-continuous (see [9] for details), but for β in a residual set of full Lebesgue measure (although the complement has full Hausdorff dimension) the corresponding β-shift does not satisfy specification (see [12]).”
AN INTRODUCTION TO QUANTITATIVE POINCARÉ RECURRENCE IN DYNAMICAL SYSTEMS (2009, unknown): “For a general account on equilibrium states, and a proof of these results, we refer to [10, 40].”