Topological pressure and large deviations for multivariate potentials

Given a topological dynamical system (X,T), this paper investigates the topological pressure and large deviation estimate for multivariate potentials Φ:={Snφ}n≥1, where φ is a real-valued continuous function on Xk andSnφ(x)=1nk−1∑i1=0n−1∑i2=0n−1⋅⋅⋅∑ik=0n−1φ(Ti1x,Ti2x,⋅⋅⋅,Tikx),x∈X. As an application, this paper finally discusses the properties of the topological pressure for the following multivariate functiong˜s(x,y):=−s12(g(x)−g(y))2,s≥0, where g:X→X is a continuous function.