This thesis investigates seveval problems about discrete fractal indices and their intrinsic relationships in Euclidean lattice and Euclidean space, and some problems in local bifurcation problems of one state variable with Z2 - symmetry.

• 本文研究欧几里得格和欧几里得空间中有关离散分形指标及其内蕴关系，和Z_2对称分岔理论中的若干问题。