Variational principle and zero temperature limits of asymptotically (sub)-additive projection pressure

摘要

Let $${S_i}_{i=1}^l$$ { S i } i = 1 l be an iterated function system (IFS) on ℝ_( d )with an attractor K . Let (∑, σ) denote the one-sided full shift over the finite alphabet {1, 2,..., l }, and let π : ∑ → K be the coding map. Given an asymptotically (sub)-additive sequence of continuous functions ℱ = { f ~( n )}~( n )⩾1; we define the asymptotically additive projection pressure P ~(π)(ℱ) and show the variational principle for P ~(π)(ℱ) under certain affne IFS. We also obtain variational principle for the asymptotically sub-additive projection pressure if the IFS satisfies asymptotically weak separation condition (AWSC). Furthermore, when the IFS satisfies AWSC, we investigate the zero temperature limits of the asymptotically sub-additive projection pressure P ~(π)( β ℱ) with positive parameter β .