Estimating the Correlation Dimension from a Chaotic System with Dynamic Noise
نویسندگان
چکیده
where F (x) = t(F (x), x1, . . . , xd−1) for x = (x1, x2, . . . , xd). Assuming Y t ∈ Ω for closed Ω ⊆ R and also assuming the ergodicity of {Y t}, we formulate the system as (Ω,F , μ,F ), where F is the completion of the Borel σ-field with respect to μ, and μ is an invariant measure, i.e. μ(F−1A) = μ(A) for A ∈ F . See Carlsson (2002) for a description of the sufficient conditions for the existence of the unique invariant measure. This paper is concerned with the correlation dimension which is defined by Grassberger and Procaccia (1983a, b) as follows. Putting
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