Abstract
We shall describe a method to calculate the Hausdorff dimension of a set of sequences of some type, by using Perron-Probenius theory of non-negative matrices. It is applied to a fractal set which is not self-similar but is a subset of the invariant set with respect to an iterated function system. It is also applied to images of certain function systems which do not satisfy the open set condition.
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References
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Dedicated to Prof. T. Ando on the occasion of his sixtieth birthday.
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© 1993 Springer Basel AG
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Takeo, F. (1993). Hausdorff Dimension of Some Fractals and Perron-Frobenius Theory. In: Furuta, T., Gohberg, I., Nakazi, T. (eds) Contributions to Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 62. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8581-2_11
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DOI: https://doi.org/10.1007/978-3-0348-8581-2_11
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9690-0
Online ISBN: 978-3-0348-8581-2
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