Certain geometric properties of self-affine fractals

• Thesis title in English: Certain geometric properties of self-affine fractals
• Key words: affine mapping, affine dynamical system, self-affine set, Hausdorff measure, Hausdorff dimension, attractor, connectivity
• English key words: affine mapping, affine dynamical system, self-affine set, Hausdorff measure, Hausdorff dimension, attractor, connectivity
• Academic year of topic announcement: 2011/2012
• Thesis type: dissertation
• Thesis language: angličtina
• Department: Mathematical Institute of Charles University (32-MUUK)
• Supervisor: prof. RNDr. Jan Rataj, CSc.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 26.09.2012
• Date of assignment: 26.09.2012
• Confirmed by Study dept. on: 05.12.2012

Guidelines

Student nastuduje zakladni literaturu k fraktalni geometrii, zejmena teorii fraktalu generovanych afinnimi systemy kontrakci. Pote aplikuje zname vysledky o dimenzi a dalsich charakteristikach pro specialni tridy techto mnozin, zejmena pro mnoziny generovane systemy aplikovanymi ve vypocetni geometrii. Nasledne se student pokusi odvodit pro tyto tridy fraktalu dalsi geometricke vlastnosti.

References

G.A. Edgar: Measure, Topology and Fractal Geometry, 2nd ed., Springer, 2008

K. Falconer: Fractal Geometry, 2nd ed., J. Wiley, 2003