TOPOLOGICAL PRESSURE OF THE SET OF GENERIC POINTS FOR Zd-ACTIONS

Abstract

Abstract. We show that, if a continuous+ -action of a compact metric space has the almost product property (which is weaker than the specification property), then, for any continuous function and any invariant measure, the topological pressure of the set of all generic points coincides with the sum of the metric entropy and the mean of the continuous function.

Multifractal analysis of ergodic averages in some non-uniformly hyperbolic systems

“…The upper bound on P (K(ϕ, α), ψ) is easy to get. However, in order to obtain the lower bound on P (K(ϕ, α), ψ), the dynamical system should be endowed with some mixing property such as specification by Takens & Verbitskiy [30], Tomphson [32], g almost product property by Pfister & Sullivan [28,29], Pei & Chen [26], Yamamoto [36]. Here, we will use the weak specification introduced by Varandas [34].…”

“…Recently, the topological pressures of the level sets has also been investigated. See Thompson [32], Pei & Chen [26], Yamamoto [36], Climenhaga [9] and Zhou & Chen [39,40]. The reader is referred to [1,2,3] and references therein for recent developments in multifractal analysis.…”

Large-deviation properties in some non-uniformly hyperbolic systems via Pesin theory

“…Recently, (1.1) and (1.2) are extended to topological pressure by Pei & Chen [14] and Thompson [19], respectively. See Yamamoto [22] for higher version and Feng & Huang [7] for sub-additive case. The investigation of multifractal analysis for nonuniformly hyperbolic systems has attracted more and more attentions.…”

Multifractal analysis for the historic set in topological dynamical systems

“…This article is devoted to investigate the structure of D(T, Ξ) via the following framework introduced and developed by Olsen [14], [15], [16], [17] and Olsen & Winter [18]. Previous studies [2], [3], [9], [21], [25], [28], [29], [33] have obtained a number of fruitful results regarding different quantities to describe the size of (1.1) in some dynamical systems with some mixing properties. The quantities include Hausdorff dimension, packing entropy, topological entropy and topological pressure.…”

“…Previous studies [2], [3], [9], [21], [25], [28], [29], [33] have obtained a number of fruitful results regarding different quantities to describe the size of (1.1) in some dynamical systems with some mixing properties. The quantities include Hausdorff dimension, packing entropy, topological entropy and topological pressure.…”