A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a
smooth action of the reals or the Integers on another object (usually a Manifold). When the reals
are acting, the system is called a continuous dynamical system, and when the Integers are acting, the
system is called a discrete dynamical system. If is any Continuous Function, then the evolution of a variable
can be given by the formula

(1) |

(2) |

(3) |

(4) |

(5) |

**References**

Aoki, N. and Hiraide, K. *Topological Theory of Dynamical Systems.* Amsterdam, Netherlands: North-Holland,
1994.

Golubitsky, M. *Introduction to Applied Nonlinear Dynamical Systems and Chaos.* New York: Springer-Verlag, 1997.

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

Lichtenberg, A. and Lieberman, M. *Regular and Stochastic Motion, 2nd ed.*
New York: Springer-Verlag, 1994.

Ott, E. *Chaos in Dynamical Systems.* New York: Cambridge University Press, 1993.

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

Strogatz, S. H. *Nonlinear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry, and Engineering.*
Reading, MA: Addison-Wesley, 1994.

Tabor, M. *Chaos and Integrability in Nonlinear Dynamics: An Introduction.* New York: Wiley, 1989.

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1999-05-24