Dynamics Links

From Iterated Functions

Dynamics Links[edit]

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 Gives an overview of my work, but is not peer-reviewed.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>