Using chaos to shadow the quadratic map for all time

Abstract

We present a new way of proving that a computer-generated orbit for the chaotic attractor outside the periodic windows of the quadratic map can be shadowed for all time (i.e., there exist true orbits which stay near a numerical orbit for all time). This is done by computing a numerical orbit for a particular value of a and show that

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The true orbits are found using slightly different maps

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This technique can therefore be applied to other chaotic differential equation and discrete systems.

Keywords:

• Chaotic trajectories
• attractors
• shadowing
• quadratic map

C.R. Categories::

• G.1
• I.6
• J.2