 Topological transitivity is the following notion: consider open sets \(U\) and \(V\) around the points \(u\) and \(v\) respectively. Regardless how small \(U\) and \(V\) are, some trajectory initiating from \(U\) eventually visits \(V\). This condition roughly guarantees that trajectories starting from points in \(U\) will eventually fill \(S\) densely. Taken together, these three conditions represent an attempt to precisely characterize the kind of irregular, aperiodic behavior we expect chaotic systems to exhibit. 