TY  - THES
AB  - In this thesis, we offer an investigation of the vibrational properties of discrete one-dimensional systems with an underlying fractal structure. Thus, the primary objects of scrutiny in this work are two types of fractal objects: the first class being quite simple structures with a fractal boundary, the second class having an internal fractal structure but very simple boundaries. By introducing a matrix representation of the related Laplacians, we prove the efficiency of using techniques originally taken from random matrix theory in the area of fractal geometry. Thereby, a unifying framework for the study of these systems has been developed, capable of being extended to higher dimensions.
AU  - Etienne, Roland Jean
DA  - 2014
KW  - Eigenwert
KW  - Eigenvalues
KW  - Laplace-Operator
KW  - Fractals
KW  - Asymptotics
KW  - Matrices
LA  - eng
PY  - 2014
TI  - On the asymptotic distribution of the Dirichlet eigenvalues of fractal chains
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:467-8700
Y2  - 2024-11-22T08:01:01
ER  -