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On Effective Banach-Mazur Games and an Application to the Poincaré Recurrence Theorem for Category

Authors Prajval Koul , Satyadev Nandakumar

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LIPIcs.STACS.2026.61.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • Recurrence
  • Topology
  • Category
  • Computable Analysis
  • Computable Toplogy
  • Dynamical Systems

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Abstract

The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we provide a game-theoretic proof of an effective theorem in dynamical systems, namely the category version of Poincaré Recurrence. The Poincaré Recurrence Theorem for category states that for a homeomorphism without open wandering sets, the set of non recurrent points forms a first category (meager) set. As an application of the effectivization of the Banach-Mazur game, we show that such a result holds true in effective settings as well.

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Prajval Koul and Satyadev Nandakumar. On Effective Banach-Mazur Games and an Application to the Poincaré Recurrence Theorem for Category. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.61

Author Details

Prajval Koul
  • Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh, India
Satyadev Nandakumar
  • Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh, India

Acknowledgements

The authors thank anonymous referees for their valuable comments on an earlier draft of this paper.

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