A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature

Keith Burns, Dong Chen

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For any rank 1 nonpositively curved surface (Formula presented.), it was proved by Burns-Climenhaga-Fisher-Thompson that for any (Formula presented.), there exists a unique equilibrium state (Formula presented.) for (Formula presented.), where (Formula presented.) is the geometric potential. We show that as (Formula presented.), the weak-* limit of (Formula presented.) is the restriction of the Liouville measure to the regular set.

Original languageEnglish (US)
Pages (from-to)1-4
Number of pages4
JournalDynamical Systems
Issue number1
StatePublished - 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Computer Science Applications

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