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arxiv:2509.02070
Finite random iterated function systems do not always satisfy Bowen's formula
Published on Sep 2
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Abstract
A counterexample demonstrates that Bowen's formula does not hold for a random iterated function system satisfying the open set condition, indicating that results for random recursive constructions do not always extend to random iterated function systems.
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In this paper, we provide a finite random iterated function system satisfying the open set condition, for which the random version of Bowen's formula fails to hold. This counterexample shows that analogous results established for random recursive constructions are not always obtained for random iterated function systems.
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