Bibliography & Credits

Primary References

The mathematical core of the solver and articles is still grounded in the following two papers:

Vladimir V. Kruchinin, Dmitry V. Kruchinin (2013). Composita and its Properties. arXiv:1103.2582v2.
arXiv:1103.2582 — Introduces the composita \(F^{\Delta}(n,k)\), proves the recurrence formula, and establishes the composition theorem used in the calculator.
Dmitry V. Kruchinin, Vladimir V. Kruchinin (2013). Method for solving an iterative functional equation \(A^{2^n}(x) = F(x)\). arXiv:1302.1986v2.
arXiv:1302.1986 — Extends the composita method to iterative functional equations and motivates the paper-depth mode in the upgraded solver.

The new analytic fixed-point mode and the blog articles use the following references to frame what is supported locally and what remains subtle.

Gabriel Koenigs (1884). Recherches sur les intégrales de certaines équations fonctionnelles. — Classical source behind local linearization by Schröder coordinates near non-parabolic fixed points.
Marek Kuczma, Bogdan Choczewski, Roman Ger (1990/2008). Iterative Functional Equations. Cambridge University Press. — Standard reference for the existence, uniqueness, and structural theory of iterative functional equations.
V. V. Goryainov (2002). Koenigs function and fractional iterates of probability generating functions.
MathDoc entry — Connects Koenigs coordinates to fractional iteration and explains how local conjugacy becomes a practical iteration tool.
Hellmuth Kneser (1950). Reelle analytische Lösungen der Gleichung \(\varphi(\varphi(x)) = e^x\). — Classical benchmark for the half-exponential problem and a reminder that global analytic roots are subtler than local series models.

Lars Regløs. \(f(f(x))\) — Interactive exploration of functional square roots.
reglos.de/lars/ffx.html — A visual counterpart to the site's focus on half-iterates and graphical experimentation.

CarlXerophilem — site design, implementation, and curation
V.V. Kruchinin & D.V. Kruchinin — the composita framework and iterative-equation method
Gabriel Koenigs, Hellmuth Kneser, Marek Kuczma and collaborators — local and global theory of fractional iteration
Lars Regløs — interactive functional-equation visualization
The page format remains adapted from the Complex Analysis online textbook by Juan Carlos Ponce Campuzano