Generalized iteration, catastrophes and generalized Sharkovsky's ordering
Dynamical Systems
2008-03-08 v2
Abstract
We define iteration of functions that map n-dimensional vector spaces into m-dimensional vector spaces (m at most equal to n). It happens that usual iteration and Fibonacci iterative methods become special cases of this generalized iteration. Mathematical objects such as orbits, bifurcations, chaos, Feigenbaum constant, (generalized) Sharkovsky ordering, (generalized) Julia and Mandelbrot sets and a new kind of catastrophe can be found and studied in this enlarged context.
Cite
@article{arxiv.0801.3755,
title = {Generalized iteration, catastrophes and generalized Sharkovsky's ordering},
author = {Andrei Vieru},
journal= {arXiv preprint arXiv:0801.3755},
year = {2008}
}
Comments
10 pages