today the image of a permanent skeletal space of cities affected by some forces or mechanisms is put in time with social-economic development and while imposes a new face and perspective to physical anatomy of cities, and prepares field to changes in content and social- economic structures of cities too. simultaneously with quitting villages in order to settle in cities by villagers, the phen...

in chapter one we will describe definitions and preliminary results to provide the global context of our own results to be presented in detail in the subsequent chapters in chapter two we consider degree-one maps of the circle and we study their rotation set. our main result in this chapter says that if the map is topologically mixing then its rotation interval is nontrivial (that is, not reduc...