Dynamics
Please see Lars Kindermann's
Iterative Roots and Fractional Iteration
web page for a comprehensive resource for fractional iteration.
For more references on continuous iteration, see the web sites of researchers in tetration. 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
S. Smale.
Differential Dynamical Systems.
Bull Amer Math Soc, 73, 1967.
Nicholas B. Tufillaro
Flows in 3D and beyond
Thursday 2PM, 22 June 1995 HPLABS Bristol, UK.
S. Rabinovich, G. Berkolaiko, S. Buldyrev, A. Shehter, and S. Havlin,
Logistic map: An analytical solution,
Phys. A 218 1995 , 457460.
Nicholas B. Tufillaro
Dynamical Systems Theory
www.drchaos.net 1997
S.C. Woon,
Analytic Continuation of Operators  Operators acting complex stimes,
arxiv.org 1997
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) 8190 (1998)
P. Gralewicz and K. Kowalski,
Continuous time evolution from iterated maps and Carleman linearization,
arxiv.org 2000
R Aldrovandi,
SPECIAL MATRICES OF MATHEMATICAL PHYSICS  Stochastic, Circulant and Bell Matrices,
World Scientific Publishing 2001
Stephen Wolfram,
A NEW KIND OF SCIENCE
Wolfram Media (2002)
Stephen Wolfram,
A NEW KIND OF SCIENCE Open Problems and Projects
http://www.wolframscience.com
A reply to one of Stephen Wolfram's questions.
Gives an overview of my work, but is not peerreviewed. See
All is Arithmetic
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.
Dynamics And Hierarchies
Iterated Sine Function
Dynamical Derivatives of Iterated Functions with Hyperbolic Fixed Points
