Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds

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Abstract:

If M is a compact Riemannian manifold then we show that for typical continuous function defined on M, the upper box dimension of  graph(f) is as big as possible and the lower box dimension of graph(f) is as small as possible.  

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volume 13  issue 2

pages  93- 99

publication date 2018-10

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