Let
be a one-parameter family of maps satisfying

Then there are intervals , , and such that

- 1. If , then has one unstable fixed point and one stable orbit of period two for , and
- 2. If , then has a single stable fixed point for .

**References**

Rasband, S. N. *Chaotic Dynamics of Nonlinear Systems.* New York: Wiley, pp. 27-30, 1990.

© 1996-9

1999-05-26