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On induced systems and ergodicity for holomorphic correspondences

  • Sathi Trikkadeeri Mana
  • Shrihari Sridharan
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Abstract

The Poincaré recurrence theorem for a holomorphic correspondence provides a natural framework for studying the first return time and a dynamical system thus induced, in this setting. After establishing a version of the Kac's theorem on the average of the first return times for a holomorphic correspondence, we introduce the concept of an induced correspondence, akin to the case of dynamics of maps and prove that it inherits the ergodicity of the holomorphic correspondence. Additionally, we characterise the ergodic measures with respect to the considered holomorphic correspondence, establish the density of forward orbits under mild conditions and prove a Rokhlin-Kakutani type lemma.

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Cite

BibTeXRIS
BibTeX
@misc{mana2026induced,
  title = {{On induced systems and ergodicity for holomorphic correspondences}},
  author = {Sathi Trikkadeeri Mana and Shrihari Sridharan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29439},
  eprint = {2609.29439},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29439},
}
RIS
TY  - UNPB
TI  - On induced systems and ergodicity for holomorphic correspondences
AU  - Sathi Trikkadeeri Mana
AU  - Shrihari Sridharan
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29439
UR  - https://arxiv.org/abs/2609.29439
AB  - The Poincaré recurrence theorem for a holomorphic correspondence provides a natural framework for studying the first return time and a dynamical system thus induced, in this setting. After establishing a version of the Kac's theorem on the average of the first return times for a holomorphic correspondence, we introduce the concept of an induced correspondence, akin to the case of dynamics of maps and prove that it inherits the ergodicity of the holomorphic correspondence. Additionally, we characterise the ergodic measures with respect to the considered holomorphic correspondence, establish the density of forward orbits under mild conditions and prove a Rokhlin-Kakutani type lemma.
ER  -