UCSC: Porter 34B, Chaos, Fractals, and the Arts, Winter 2016

Homework 09. Assigned Wednesday March 02, 5 pm

Deadline for this assignment is 8 am on Tuesday morning, 3/08/16.

B. Chaos theory.

Please give brief answers to these questions, based on the readings assigned for thread B in HW-02.

Let D be a rectangle in a plane, and p a point of D.

  1. Define an iteration (aka semi-cascade, or discrete dynamical system) on D.
  2. Given an iteration on D, what is the trajectory of p?
  3. Given an iteration on D, what is the orbit of p?
  4. Given an iteration on D, what is an attractor?
  5. Given an iteration on D, define a periodic (or cyclic) attractor.
  6. Given a periodic attractor of an iteration, what is its period?

Back to the Index for Meeting 09
Revised 02 mar 2016 by Ralph