The Topological Pressure On The Irregular Set For Almost Additive Potentials

Let(X,T) be a topological dynamical system(TDS for short) in the sense that X is a compact metric space with the metric d and T:X→X is a continuous map.In this paper,we consider a TDS with the specification property,and a sequence of almost additive continuous functions,we define the irregular set for it(in the sense of sub-additive ergodic theorem) and show that this irregular set is either empty or carries full almost additive topological pressure.We adopt Thompson's methods of the construction Of the fractal and the good measures,using the distribution of the topological pressure to prove the desired results.