Spurious Lyapunov Exponents in Attractor Reconstruction

Abstract

Lyapunov exponents, perhaps the most informative invariants of a complicated dynamical process, are also among the most difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra {open_quotes}spurious{close_quotes} Lyapunov exponents arise that are not Lyapunov exponents of the original system. The origin of these spurious exponents is discussed, and formulas for their determination in the low noise limit are given. {copyright} {ital 1998} {ital The American Physical Society}