On the Validity of the 0-1 Test for Chaos
Georg A. Gottwald, Ian Melbourne
TL;DR
This paper provides a theoretical foundation for the 0-1 test for chaos, confirming its reliability in distinguishing between periodic, quasiperiodic, and chaotic systems.
Contribution
It offers a rigorous proof that the 0-1 test accurately classifies dynamics with probability one, strengthening its theoretical basis.
Findings
The test yields 0 for periodic and quasiperiodic systems.
The test yields 1 for sufficiently chaotic systems.
The results are valid with probability one.
Abstract
In this paper, we present a theoretical justification of the 0-1 test for chaos. In particular, we show that with probability one, the test yields 0 for periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics.
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