Abstract:We consider a semidynamical system $(X,\Cal B,\Phi ,w)$. We introduce the cone $\Bbb A$ of continuous additive functionals defined on $X$ and the cone $\Cal P$ of regular potentials. We define an order relation ``$\leq $'' on $\Bbb A$ and a specific order ``$\prec $'' on $\Cal P$. We will investigate the properties of $\Bbb A$ and $\Cal P$ and we will establish the relationship between the two cones.
Keywords: additive functional, excessive functions, regular potential, semidynamical system, specific order
AMS Subject Classification: Primary 58F98, 31D05; Secondary 60J55, 60J45