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Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Nov;78(5 Pt 2):056203. Epub 2008 Nov 7.

When Lyapunov exponents fail to exist.

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1
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.

Abstract

We describe a simple continuous-time flow such that Lyapunov exponents fail to exist at nearly every point in the phase space R2 , despite the fact that the flow admits a unique natural measure. This example illustrates that the existence of Lyapunov exponents is a subtle question for systems that are not conservative.

PMID:
19113196
DOI:
10.1103/PhysRevE.78.056203
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