Title of article :
Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds
Author/Authors :
Mirzaie, Reza Department of Pure Mathematics - Faculty of Science - Imam Khomeini International University - Qazvin, Iran
Abstract :
If M is a compact Riemannian manifold and C(M;R) is the
set of all real valued continuous functions dened on M, then we show
that for a typical element f 2 C(M;R), dimB(graph(f)) is as big as
possible and for a typical f 2 C(M;R), dimB(graph(f)) is as small as
possible.
Keywords :
Box dimension , Fractal , Manifold
Journal title :
Astroparticle Physics
