Chapter 9, Exploration 15

Use the tool to zoom in on the period 3 window (use $$3.8 < a < 3.87)$$ at first but you may need to narrow this range as you work through this exercise).

• What happens to the period 3 orbit as $$a$$ increases through this range? In other words, what attracting periodic orbits are descended'' from the original periodic orbit.
• How does this relate to what you observed in section 9.3?
• Find some other windows of stable periodic behavior and again zoom in on it. What do you notice?
• Do you have any ideas about why the period 3 orbit "suddenly" appears from the chaotic chaotic behavior?