caa a22 4500 386377685 CHVBK 20180307112027.0 cr unu---uuuuu 161130e198909 xx s 000 0 eng 10.1017/S0143385700005162 doi S0143385700005162 pii (NATIONALLICENCE)cambridge-10.1017/S0143385700005162 Rand D. A. Nonlinear Systems Laboratory, Mathematics Institute, Warwick University, Coventry CV4 7AL, UK The singularity spectrum f(α) for cookie-cutters [Elektronische Daten] [D. A. Rand] I use a thermodynamic formalism to study the spectrum f(α) which characterises the large fluctuations of pointwise dimension in a Gibbs state supported on a hyperbolic cookie-cutter. Amongst other things, it is proved thatf(α) is the Hausdorff dimension of the set of points with pointwise dimension α, that f(α) is real-analytic and that its Legendre transform τ(q) is related to the Renyi dimension Dq of the Gibbs state by the formula (1 − q)Dq = τ(q). Copyright © Cambridge University Press 1989 Ergodic Theory and Dynamical Systems Cambridge University Press 9/3(1989-09), 527-541 0143-3857 9:3<527 1989 9 ETS https://doi.org/10.1017/S0143385700005162 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0143385700005162 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rand D. A. Nonlinear Systems Laboratory, Mathematics Institute, Warwick University, Coventry CV4 7AL, UK NATIONALLICENCE 773 0- Ergodic Theory and Dynamical Systems Cambridge University Press 9/3(1989-09), 527-541 0143-3857 9:3<527 1989 9 ETS CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge