Density of the Periodic Points in the Interval Set


Mathematics department, Faculty of science, Shahid Rajaee Teacher Training University, Tehran, Iran.


The dynamical system (f,R) is introduced and some of its properties are investigated. It is proven that there is an invariant set Λ on which the periodic points of f are dense.


1. R. Devaney, An introduction to chaotic dynamical systems, 2nd. ed., Addison-Wesley, (1989).

2. S. N. Elaydi , Discrete chaos, with applications in science and engineering, 2nd. ed., Chapman and Hall/CRC, (2007).

3. R.L. Kraft, Chaos, Cantor sets, and Hyperbolicity for the Logistic Maps, The American Mathematical Monthly, vol.106, no.5, (1999), 400-408,

4. W. de Melo , S. van Strien, One-dimensional dynamics, Springer-Verlag, (1993).