2016
DOI: 10.4172/2090-0902.1000199
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On Discretizations of the Generalized Boole Type Transformations and their Ergodicity

Abstract: There is studied an analytical discretization of the generalized Boole type transformations in ℝn and their ergodicity properties.The fixed points of the corresponding finite-dimensional stochastic Frobenius-Perron operator discretization are constructed, the structure of the related invariant measures is analyzed.

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Cited by 2 publications
(4 citation statements)
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References 12 publications
(31 reference statements)
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“…owing to changing the variables x = cot(πs), y = cot(πt), (s, t) ∈ [0, 1) 2 , (x, y) ∈ R 2 , subject to the new coordinates (s, t) ∈ [0, 1) 2 and the transformation S −1 : [0, 1) 2 (s, t) → ({s + t}, {s − t}) ∈ [0, 1) 2 . That this approach could be used to prove of the ergodicity theorem of the two-dimensional Boole transformation (73), was announced in [70][71][72] and is now confirmed by the following result.…”
Section: Multi-dimensional Boole Transformations: Their Entropy and Ergodicitymentioning
confidence: 68%
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“…owing to changing the variables x = cot(πs), y = cot(πt), (s, t) ∈ [0, 1) 2 , (x, y) ∈ R 2 , subject to the new coordinates (s, t) ∈ [0, 1) 2 and the transformation S −1 : [0, 1) 2 (s, t) → ({s + t}, {s − t}) ∈ [0, 1) 2 . That this approach could be used to prove of the ergodicity theorem of the two-dimensional Boole transformation (73), was announced in [70][71][72] and is now confirmed by the following result.…”
Section: Multi-dimensional Boole Transformations: Their Entropy and Ergodicitymentioning
confidence: 68%
“…where a, b j ∈ R, j = 1, N, α, β j ∈ R + , j = 1, N, and analyzed in [1,3,11,72,73]. For α = 1, a = 0, the ergodicity result was proved in [3,[74][75][76] by making use of a specially devised inner function method.…”
Section: One-dimensional Boole-type Mappings Invariant Ergodic Measures and Their Entropiesmentioning
confidence: 99%
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