Topological pressure for holomorphic correspondences using open covers

TL;DR

This paper introduces a new way to define topological pressure for holomorphic correspondences on the Riemann sphere using open covers, aligning with existing orbit-based definitions.

Contribution

It presents a novel approach to topological pressure for holomorphic correspondences via open covers, bridging it with traditional orbit-based methods.

Findings

The new definition coincides with existing orbit-based pressure definitions.

Provides a unified framework for topological pressure in holomorphic dynamics.

Enhances understanding of dynamical invariants using open covers.

Abstract

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.