Year: 2021
Type: preprint
Abstract: Using infinite compositions, we solve the general equations $P(λw) = p(w)f(P(w))$ for holomorphic functions $p$ and $f$. We describe the situations in which this equation is palpable; and their effectiveness at describing dynamical properties of the orbit $f^{\circ n}(z)$. We similarly make a change of variables to study a generalized form of the Abel equation, $F(s+1) = u(s)f(F(s))$. This paper is intended as a more in depth examination of work done previously in our last paper--The Limits of a Family; Of Asymptotic Solutions to the Tetration Equation.
Source: arXiv (Cornell University)
Author: Nixon, James David
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3196878615