Variational Priciple And Zero Temperature Limits Of Non-additive Projective Pressure

Let{Si)i=1l be an iterated function system(IFS)on Rd with an attractor K.Let (∑,σ)denote the one-sided full shift over the finite alphabet{1,2,…,l] and let Ï€:∑â†' K be the coding map.Given a non-additive sequence of continuous functions F={fn) on ∑,this paper defines non-additive projection pressure PÏ€(F)and shows the variational principle for PÏ€(F)under certain IFS which is affine and/or satisfies asymptotically weak separation condition(AWSC).Furthermore,if the IFS{Si}i=1l satisfies AWSC this paper investigates the zero temperature of the non-additive projection pressure PÏ€(βF)with positive parameter β.