File:Markus-Ljapunow Exponent 8.jpg

Uploaded by Mario Markus
Upload date 2022-09-28T19:00:16Z
MIME type image/jpeg
Dimensions 3276 × 3830 px
File size 4.7 MB

Summary

Description
English: The picture was constructed with an iterative equation of the form xn+1=f(r,xn),n=1,2,3..., where r is a parameter that varies periodically between two values A and B. An exponent on A or B indicates a consecutive repetion of A or B, as given by the exponent. Example: A with exponent 4 means to be an r-sequence AAAA. The parameter A corresponds to the x-axis of the picture and B to the y-axis. f is given by te following formula:

xn+1={bsin2(xn+r)+αrkif [xn]mod(π)<π2bsin2(xn+r)+βrkelse 
r:A7B7 A7B7...,b=2.36,β=0.16

The exponential growth of a small perturbation is determined for each point in the picture, i.e. for each pair (A,B). The value of the resulting exponent (Markus-Lyapunov exponent) is show with a color.
Date
Source Own work
Author Mario Markus

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1 January 2017

image/jpeg

4,920,536 byte

3,830 pixel

3,276 pixel

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