On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions |
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| Authors: | Ya. B. Pesin |
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| Affiliation: | (1) Department of Mathematics, Pennsylvania State University, 16802 University Park, Pennsylvania |
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| Abstract: | We consider different definitions of the correlation dimension and find some relationships between them and other characteristics of dimension type such as Hausdorff dimension, box dimension, etc. We also introduce different ways to define and study the generalized spectrum for dimensions—a one-parameter family of characteristics of dimension type. |
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| Keywords: | Dimension correlation dimension Hausdorff dimension box dimension generalized spectrum of dimensions |
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