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1
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Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

100%
Roychowdhury M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2013
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tom 61
|
nr 1
35-45
EN
We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show that for a given r ∈ (0,∞) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension $D_r(ν)$ of ν and bounded above by a unique number $κ_r ∈ (0,∞)$, related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.
2
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Quantization Dimension Function and Ergodic Measure with Bounded Distortion

100%
Roychowdhury M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
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tom 57
|
nr 3
251-262
EN
The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.
3
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Lower quantization coefficient and the F-conformal measure

100%
Roychowdhury M.
Colloquium Mathematicum
|
2011
|
tom 122
|
nr 2
255-263
EN
Let $F = {f^{(i)} : 1 ≤ i ≤ N}$ be a family of Hölder continuous functions and let ${φ_i: 1 ≤ i ≤ N}$ be a conformal iterated function system. Lindsay and Mauldin's paper [Nonlinearity 15 (2002)] left an open question whether the lower quantization coefficient for the F-conformal measure on a conformal iterated funcion system satisfying the open set condition is positive. This question was positively answered by Zhu. The goal of this paper is to present a different proof of this result.
4
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The Morse minimal system is finitarily Kakutani equivalent to the binary odometer

63%
Roychowdhury M., Rudolph D.
Fundamenta Mathematicae
|
2008
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tom 198
|
nr 2
149-163
EN
Two invertible dynamical systems (X,𝔄,μ,T) and (Y,𝔅,ν,S), where X and Y are Polish spaces and Borel probability spaces and T, S are measure preserving homeomorphisms of X and Y, are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping ϕ from a subset X₀ of X of measure one onto a subset Y₀ of Y of full measure such that (1) $ϕ|_{X₀}$ is continuous in the relative topology on X₀ and $ϕ^{-1}|_{Y₀}$ is continuous in the relative topology on Y₀, (2) $ϕ(Orb_{T}(x)) = Orb_{S}(ϕ(x))$ for μ-a.e. x ∈ X. (X,𝔄,μ,T) and (Y,𝔅,ν,S) are said to be finitarily evenly Kakutani equivalent if they are finitarily orbit equivalent by a mapping ϕ for which there are measurable subsets A of X and B = ϕ(A) of Y with ϕ an isomorphism of $T_{A}$ and $T_{B}$. It is shown here that the Morse minimal system and the binary odometer are finitarily evenly Kakutani equivalent.
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