Dynamics

Please see Lars Kindermann's Iterative Roots and Fractional Iteration web page for a comprehensive resource for fractional iteration.

Resources for continuous iteration

S. Smale.
Differential Dynamical Systems.
Bull Amer Math Soc, 73, 1967.

Nicholas B. Tufillaro
Flows in 3-D and beyond
Thursday 2PM, 22 June 1995 HP-LABS Bristol, UK.

S. Rabinovich, G. Berkolaiko, S. Buldyrev, A. Shehter, and S. Havlin,
Logistic map: An analytical solution,
Phys. A 218 1995 , 457-460.

Nicholas B. Tufillaro
Dynamical Systems Theory
www.drchaos.net 1997

S.C. Woon,
Analytic Continuation of Operators - Operators acting complex s-times,
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) 81-90 (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 Gives an overview of my work, but is not peer-reviewed. 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

Contact:

daniel@tetration.org