I am looking for more words or phrases for "marked by". For example:
The post industrial revolution history is marked by rapid urbanisation and an exponential growth in population.
Please suggest good alternative words and phrases to replace marked by in the above sentence; and can characterised by be substituted for marked by?
Yes, "characterised by" works fine there. In some cases you can also say "distinguished by," but that option works best when there's at least an implicit contrast. For example, you might say,
While the interwar period was marked by economic stagnation, the postwar period was distinguished by productivity gains and rapid growth.
You can also rephrase and say x was the hallmark of z, or x and y were hallmarks of z, like this
Productivity gains and rapid economic growth were hallmarks of the postwar years.
But this only works if the gains and growth were at least fairly pronounced or notable. (You can't say "low unemployment was the hallmark of the 1960s" if unemployment was about equally low in the 1950s and the 1970s, though you can say "the 1960s continued to be marked by/characterised by low unemployment.")
