Topological pressure of free semigroup actions under a mistake function for non-compact sets
Topological pressure is a core concept of dynamic systems and ergodic theory,which plays an important role in the study of thermodynamic formalism. As the physical process evolves,it is natu-ral for the evolution process to produce changes or some errors in the orbit calculation. However,a self-adaptable system should decrease errors over time. In this paper,we introduce two definitions of topological pressure of free semigroup actions under a mistake function by using C-P structure and prove that they are equivalent. Furthermore,we show that the topological pressure of free semigroup actions under a mistake function on a non-compact subset is equivalent to the topological pressure of free semigroup actions of the subset without mistake function. As an application,we use the above theorem to show that the topological pressure of free semigroup actions defined by mean metric is equivalent to the topological pressure of free semigroup actions defined by Bowen metric.
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