arXiv subjects
Publications and source records attributed to Subith Gopinathan.
In this paper, we define the topological pressure of continuous functions with respect to the holomorphic correspondences using the open covers of the Riemann sphere. Further, we show that this method coincides with the existing definition of pressure that uses the notion of separated and spanning family of orbits.
In this paper, we consider a dynamical system on the Riemann sphere that evolves through a set-valued map, namely a holomorphic correspondence. Analogous to the investigation of the dynamics effected by a continuous map defined on a compact metric space, wherein the concept of measure-theoretic entropy of the map and its utility in defining the pressure of a function are well-studied, we define the measure-theoretic entropy of a holomorphic correspondence and use the same to define the pressure of continuous functions. These ideas naturally lead to the formulation of a variational principle in the context of the dynamics of a holomorphic correspondence.
In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related to a finitely generated rational semigroup. To be precise, we obtain some comparability results for the above mentioned counting functions.