Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A NECESSARY AND SUFFICIENT CONDITION FOR THE EXISTENCE OF INVARIANT GIBBS MEASURES

  • Minkyu Kim (Department of Mathematics Ajou University)
  • Received : 2023.11.06
  • Accepted : 2023.12.21
  • Published : 2024.07.31
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Abstract

In this paper, we study a relation between the existence of invariant Gibbs measures and the balanced property of subshifts. We show that a subshift X has an invariant Gibbs measure for f ∈ C (X, ℝ) if and only if it is balanced with respect to f.

Keywords

Acknowledgement

This work is a part of the author's dissertation. The author would like to thank Uijin Jung for encouragement, guidance and support. I would also like to thank Kyewon Koh Park and the referee for the careful reading of my manuscript and many valuable comments which have improved the paper. This research was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2018R1D1A1B07050803).

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