A view towards mixing in holomorphic correspondences

TL;DR

This paper develops a theory of mixing and weak mixing for holomorphic correspondences on complex manifolds, linking it to ergodicity and providing examples and characterizations.

Contribution

It introduces a new framework for understanding mixing in holomorphic correspondences and connects it to existing ergodic theory, with illustrative examples and product analysis.

Findings

Established a theory of mixing and weak mixing for holomorphic correspondences.

Connected mixing notions to ergodicity theory of Londhe.

Characterized weakly mixing via product of correspondences.

Abstract

In this manuscript we develop a theory of mixing and weakly mixing in the study of dynamics of holomorphic correspondences defined on a compact connected complex manifold. We also connect these notions to the theory of ergodicity of holomorphic correspondences developed by Londhe. Further, we give motivation and illustrative examples that compare the present scenario with that of maps. Finally, we study product of two holomorphic correspondences and use them to characterise weakly mixing.