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Topological pressure for holomorphic correspondences using open covers

Subith Gopinathan

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.

Topological pressure for holomorphic correspondences 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.
Paper Structure (6 sections, 7 theorems, 37 equations)

This paper contains 6 sections, 7 theorems, 37 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Open covers for holomorphic correspondence
  4. Proof:
  5. Proof:
  6. Proof:

Key Result

Theorem 2.4

SS:2025 Let $F$ be a holomorphic correspondence defined on $\widehat{\mathbb{C}}$, as represented in Equation correspondence. Then, for any function $g \in \mathcal{C}(\widehat{\mathbb{C}},\mathbb{R})$, the topological pressure of $g$ with respect to $F$ is given by

Theorems & Definitions (10)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Theorem 2.4
  • Corollary 2.5
  • Proposition 3.1
  • Proposition 3.2
  • Lemma 3.3
  • Theorem 3.4
  • Corollary 3.5