3

According to Wolfram, a quadratic recurrence relation uses a second degree polynomial to express $x_{n+1}$ as a function of $x_n$. A "quadratic map", then, is a recurrence relation:

$$x_{n+1} = a (x_n)^2 + b x_n + c$$

Aside from Wolfram's Quadratic Map page, I can't seem to find much information on "Quadratic Maps". Is there some definitive reference on the topic, or some resource/reference that explains a lot of what is known about QMs?

Matt Groff
  • 6,117
  • @TBrendle: Yes. I didn't have much luck. I'm really hoping that I can some how get a general idea of what is known. It seems that I can only get information on special cases, but maybe that is all that is known. – Matt Groff Oct 28 '13 at 20:06
  • 2
    By a change of variable, you can reduce this to the case$$z_{n+1} = z_n^2 + d$$ –  Oct 28 '13 at 20:32
  • Yes , then download Ultra Fractal 5 ! – Alan Oct 28 '13 at 20:40

1 Answers1

3

Perhaps something like "Iterated Maps On The Interval As Dynamical Systems" by Collet and Eckmann . Additional: http://www.amazon.com/Iterated-Interval-Dynamical-Birkh%C3%A4user-Classics/dp/0817649263#reader_0817649263

Perhaps also Mira-Gumowski maps, these are generally real valued but perhaps not as simple as a quadratic map. I suggest you google the topic and view the images. Maybe that would be of interest.

Alan
  • 2,239
  • 13
  • 15