Geodesic
Ergodicity in the dynamics of holomorphic correspondences
Mayuresh Londhe1
1 Indiana University, Department of Mathematics
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 695–712.

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This paper studies ergodic properties of certain measures arising in the dynamics of holomorphic correspondences. These measures, in general, are not invariant in the classical sense of ergodic theory. We define a notion of ergodicity, and prove a version of Birkhoff's ergodic theorem in this setting. We also show the existence of ergodic measures when a holomorphic correspondence is defined on a compact complex manifold. Lastly, we give an explicit class of dynamically interesting measures that are ergodic as in our definition.
DOI : 10.54330/afm.152565
Keywords: Correspondences, ergodicity, invariant measures, equidistribution

Mayuresh Londhe 1

1 Indiana University, Department of Mathematics 
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Mayuresh Londhe. Ergodicity in the dynamics of holomorphic correspondences. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 695–712. doi : 10.54330/afm.152565. http://geodesic.mathdoc.fr/articles/10.54330/afm.152565/

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