Pressures for Asymptotically Sub-additive Potentials Under a Mistake Function

TL;DR

This paper introduces a new concept of pressure for asymptotically subadditive potentials under a mistake function, establishing a variational principle using ergodic theory and topological dynamics.

Contribution

It defines a novel topological pressure for these potentials and proves a variational principle without extra conditions on the potentials or space.

Findings

Established a variational principle for the new pressure concept

Extended pressure theory to asymptotically subadditive potentials under mistake functions

Applied ergodic theory and topological dynamics techniques

Abstract

This paper defines the pressure for asymptotically subadditive potentials under a mistake function, including the measuretheoretical and the topological versions. Using the advanced techniques of ergodic theory and topological dynamics, we reveals a variational principle for the new defined topological pressure without any additional conditions on the potentials and the compact metric space.