Topological Entropy Condition Amenable Group Action Dimension Of Dynamical Systems And Self-conformal Measure Divergent Points

This thesis inyestigares some problems of the topological con-ditional entropy in topological dynamical systems and multifrac-tal analysis.In the first part of the thesis,we will define topo-logical conditional entropy for amenable group actions and prove the variational principles for it. In the second part,we will com-pute the dimensions of divergence points of self-conformal mea-sures with the open set condition.Furthermore,it shows that the set{x∈supp μ:A(log μ(B(x,r))/logr)=I)is not Taylor fractal and the set{x∈supp μ:A(log μ(B(x,r))/logr)(?)I)is Taylor fractal.Thepaper is0rganized as followsIn chapter1,the backgrounds of topological entropy and multi-fractal analysis are introduced.In chapter2,we recall some classical definitions in topological dynamical systems and ergodic theory.In chapter3,we define topological conditional entroPy for amenable group actions and prove the variational principle for it.In chapter4,the dimensions of divergence points of self-conformal measures are investigated with the open set condition.