The study of fractional self-iterations of a map. A basic example is the analysis of functional square roots of a map $g$, i.e. solutions $f$ to the functional equation $f \circ f = g$. The continuous version of fractional iteration concerns maps which have flows. This case is also known as continuous iteration. A classic example is the problem of extending tetration to the real and complex numbers.
8 years ago
11 months ago
Joel David Hamkins
Recent Hot AnswersHow to solve $f(f(x)) = \cos(x)$?
“Closed-form” functions with half-exponential growth
Rational functions with a common iterate
Does the exponential function have a (compositional) square root?
Does the formal power series solution to $f(f(x))= \sin( x) $ converge?
real-analysis × 7
asymptotics × 5
co.combinatorics × 2
complex-dynamics × 2
conjectures × 2
taylor-series × 2more related tags