Here's a hint I got from a friend who is a chef - glass top stoves work best for heavier cookware that absorb and retain a lot of heat. The thicker and heavier, the better - that way the cycling of the heating element has less of a momentary effect over the heat inside the pan or pot. Thinner and lighter cookware that doesn't retain a lot of heat change temp too quickly as the heating elements cycle.
So long as you are careful with them, she recommends good quality (and heavy) cast iron pans on a glass top stove and you shouldn't have any issues with those rapid temp changes. Unless you drop it...
As for my own observations about "induction" cooktops, they are tricky. Yes, they are much quicker and hold a solid temperature without that annoying cycling (some even allow you to set a specific temp in degrees) which is a bonus, but if you are the type who moves or lifts a pan frequently you will have to get used to how induction works with that. Every time you remove the pan from the burner - even for a moment - many of them go into stand-by mode and you have to restart the burner when you put the pan back down.
You will need to be aware that not all pans are induction-capable. The bottom of the pan must be magnetic in order for it to work on an induction cooktop - all-aluminum, glass and ceramic pans will not work. All-carbon steel (but not necessarily stainless steel) and cast iron (even the thinner cast iron) are the best because they are ferrous throughout.
It also should be mentioned that an induction burner generates no heat of its own. If you lift a hot pan off an active burner, the only heat will be whatever is transmitted back to the burner from the hot pan. This means if you spill anything onto an empty burner - even one you were just using - nothing will burn onto the cooktop or surface.
There's my two cents worth!