Bowen's formula and the difference between random iterated function systems and random recursive constructions

Summary · qwen2.5:32b

The paper demonstrates that the difference in independence structures between random iterated function systems and random recursive constructions affects the validity of Bowen's formula, with the formula failing for certain random iterated function systems but always holding for random recursive constructions. This distinction impacts dimension theory, showing concrete implications of structural differences between these models.

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Exploring the differences between random iterated function systems and random recursive constructions in dimension theory, with focus on Bowen's formula.

Excerpt

arXiv:2509.02070v3 Announce Type: replace Abstract: In this paper, we show that the difference in independence structures between random iterated function systems and random recursive constructions is reflected in the validity of Bowen's formula. More precisely, we construct random iterated function systems for which Bowen's formula fails, whereas Bowen's formula always holds for random recursive constructions. Our construction demonstrates that the difference in independence structures between the two random models has genuine consequences for dimension theory.