# Dynamics Links

### Dynamics Links[edit]

- Bell Matrices and Continuous Iteration
- Mathematica resources

See Ioannis Galidakis' link on A Collection of References for Infinite Exponentials and Tetration and the Tetration Forum literature references database.

### Resources for continuous iteration[edit]

S. Smale.

*Differential Dynamical Systems*.

Bull Amer Math Soc, 73, 1967.

S. Rabinovich, G. Berkolaiko, S. Buldyrev, A. Shehter, and S. Havlin,

*Logistic map: An analytical solution*,

Phys. A 218 1995 , 457-460.

R. Aldrovandi and L. P. Freitas,

*Continuous iteration of dynamical maps*,

J. Math. Phys. 39, 5324 (1998)

G. Berkolaiko, S. Rabinovich, and S. Havlin,

*Analysis of Carleman Representation of Analytical Recursions*,

J. Math. Anal. Appl. 224 (1) 81-90 (1998)

P. Gralewicz and K. Kowalski,

*Continuous time evolution from iterated maps and Carleman linearization*,

arxiv.org 2000

Stephen Wolfram,

*A NEW KIND OF SCIENCE*
Wolfram Media (2002)

Stephen Wolfram,

*A NEW KIND OF SCIENCE Open Problems and Projects*

<a href="http://www.wolframscience.com">*http://www.wolframscience.com*</a>

A reply to one of Stephen Wolfram's questions.
Gives an overview of my work, but is **not peer-reviewed**. See
<a href="../Ackermann/arithmetic.html">All is Arithmetic</a>

Here are some links to my earlier work. I have put these links here solely so that I can refer researcher to information substantiating my current work. Some of this material has minor errors in it.

<a href="DynamicsAndHierarchies.htm">Dynamics And Hierarchies</a>

<a href="IteratedSine/index.html">Iterated Sine Function</a>

<a href="DynDerv/index.html">Dynamical Derivatives of Iterated Functions with Hyperbolic Fixed Points</a>