Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780429972195
Author: Steven H. Strogatz
Publisher: Taylor & Francis
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Chapter 10.3, Problem 8E
Interpretation Introduction

Interpretation:

Consider the map of the unit interval into itself. An orbit {xn} is said to be dense if it eventually gets arbitrarily close to every point on the interval. Such an orbit has to hop around rather crazily. More precisely, given any ε >0 and any point p[0,1], the orbit {xn} is dense if there is some finite n such that |xn- p| < ε.

To construct explicitly a dense orbit for the decimal shift map xn+1=10xn(mod1).

Concept Introduction:

  • ➢ The decimal shift map of the unit interval the fixed point is in the rational and irrational form which defined the stability of the map.

  • ➢ The decimal shift map of the unit interval [0,1] is xn+1 = f(xn).

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