Let be a one-parameter family of Map satisfying

then there exist intervals , and such that

- 1. If , then has two fixed points in with the positive one being unstable and the negative one stable, and
- 2. If , then has no fixed points in .

(Guckenheimer and Holmes 1997, p. 145).

**References**

Guckenheimer, J. and Holmes, P. *Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed.*
New York: Springer-Verlag, pp. 145-149, 1997.

Rasband, S. N. *Chaotic Dynamics of Nonlinear Systems.* New York: Wiley, pp. 27-28, 1990.

© 1996-9

1999-05-26