Resources for continuous iteration
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,
A NEW KIND OF SCIENCE Wolfram Media (2002)
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 Gives an overview of my work, but is not peer-reviewed.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>