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Oscillations in the Determination of Renyi Dimension
Author(s) -
Thümmel Ottfried
Publication year - 1987
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19874990809
Subject(s) - dimension (graph theory) , generalization , attractor , metric (unit) , physics , chaos (operating system) , nonlinear system , degree (music) , correlation dimension , statistical physics , mathematics , packing dimension , pure mathematics , mathematical analysis , mathematical physics , fractal dimension , minkowski–bouligand dimension , quantum mechanics , computer science , fractal , operations management , computer security , acoustics , economics
To describe the degree of chaos of a strange attractor created by a nonlinear map, G RASSBERGER [1] revived Renyi Dimension D q which is a common generalization of both metric capacity D 0 and information dimension D 1 . But often, the numerical determination of D q is complicated by an oscillating effect first investigated by B ADII and P UOLITI [5] for a dimension similar to D 0 . This effect is studied in the present paper. We consider the conditions for the appearance of oscillations and the dependence on q , and we give some numerical examples.