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# A dimension gap for continued fractions with independent digits - the non stationary case

We show there exists a constant $0

Mathematics - Dynamical Systems, 11K55 (Primary), 37C45 (Secondary), Dynamical Systems (math.DS), FOS: Mathematics

Mathematics - Dynamical Systems, 11K55 (Primary), 37C45 (Secondary), Dynamical Systems (math.DS), FOS: Mathematics

###### 11 references, page 1 of 2

x ∈ X : [BH] P.Billingsley and I.Henningsen, Hausdorff dimension of some continued-fraction sets. Z. Wahrsch. verw. Geb. 31 (1975), 163-173. [OpenAIRE]

[BHK] J.R.Blum, D.L.Hanson and L.H.Koopmans, On the Strong Law of Large Numbers for a Class of Stochastic Processes. Z. Wahrsch. verw. Geb. 2 (1963), 1-11.

[Br] R.C.Bradley, On the ψ-mixing condition for stationary random sequences. Trans. Amer. Math. Soc. 276 (1983) 55-66. MR684493.

[Ch] S.D.Chatterji, Masse, die von regelmässigen Kettenbruchen induziert sind, Math. Ann., vol. 164 (1966), pp. 113-117. MR0193079 (33:1300).

[EW] M.Einsiedler and T.Ward, Ergodic Theory with a View Towards Number Theory (Graduate Texts in Mathematics, 259). Springer, London, 2011. [OpenAIRE]

[He] L.Heinrich, Mixing properties and central limit theorem for a class of non-identical piecewise monotonic C2-transformations. Mathematische Nachricht. 181, 185-214 (1996).

[KPW] Y.Kifer, Y.Peres and B.Weiss, A dimension gap for continued fractions with independent digits. Israel J. Math. 124(1), (2001), 61-76.

[KP] J.R.Kinney and T.S.Pitcher, The Dimension of Some Sets Defined in Terms of f - expansions. Z. Wahrsch. verw. Geb. 4 (1966), 293-315

[R] A.Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hung., 8 (1957), pp. 477-493. [OpenAIRE]

[Wa1] P.Walters, Invariant measures and equilibrium states for some mappings which expand distances. Trans. Amer. Math. Soc. 236 (1975), 121-153.

- Funder: European Commission (EC)
- Project Code: 306494
- Funding stream: FP7 | SP2 | ERC

We show there exists a constant $0