Bowen's Formula for Nonirreducible Dynamical Systems

Definitions and mathematical statement

Formulation and unresolved definitions. The supplied record concerns dynamical systems described as non-irreducible and an identity called Bowen's formula. It does not specify the ambient class of dynamical systems, the meaning of irreducibility, or the particular version of Bowen's formula. These terms therefore remain unresolved; no particular phase space, map, potential, pressure, dimension, or regularity assumptions can be fixed from the supplied statement.

Problem (as supplied). Determine for which large classes of non-irreducible systems Bowen's formula holds, and whether there is a variation of Bowen's formula encompassing an even broader class of systems.

The two requested tasks are to identify classes on which the intended formula is valid and to formulate an extension with broader applicability. The source does not define what makes a class "large," which classes provide the comparison for "even broader," or what constitutes an admissible variation of the formula. Consequently, this is a research question whose fully quantified mathematical formulation requires additional source context; it does not determine a unique conjectural identity or theorem.

Short English statement

The problem asks how broadly Bowen's formula applies to non-irreducible dynamical systems and whether an extended formula applies more widely. The supplied record leaves the systems, irreducibility condition, formula, and comparison classes unspecified, so a unique precise conjecture cannot yet be stated.

Sources

• Local UnsolvedMath registry: supplied complete record with permanent ID $30001956$, title "Bowen's Formula for Nonirreducible Dynamical Systems," and exact source problem code catalogue entry, in the Oberwolfach Reports Open Problems collection.
• Supplied report citation: Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), Oberwolfach Reports, pp. 77--129, DOI 10.4171/owr/2012/03. Source URL and supplied literature reference labelled "original Oberwolfach report": https://doi.org/10.4171/owr/2012/03. The record describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions. No individual proposer is supplied; the recorded proposed year is 2012.
• Supplied dated literature curation, checked 2026-08-21: status "open." Its assessment states that the report asks for extensions of Bowen's formula to broad non-irreducible systems, and that available results cover special classes without establishing the requested broad scope. This is supplied dated curation, not an independently verified literature assessment. The record expressly requests independent verification of time-sensitive status and cited claims.
• The registry labels the statement "exact" and reports that manual review found the extracted statement self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. These are supplied verification claims; the report and its surrounding mathematical context have not been independently inspected here.