Generalized iteration, catastrophes and generalized Sharkovsky's ordering

Details Generalized iteration, catastrophes and generalized Sharkovsky's ordering Generalized iteration, catastrophes and generalized Sharkovsky's ordering

2008-01-24

arxiv.org/abs/0801.3755v2

Mathematics

Dynamical Systems

10 pages

Scientific paper

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.

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