Is the largest Lyapunov exponent preserved in embedded dynamics?

Abstract

The method of reconstruction for an n-dimensional system from observations is to form vectors of m consecutive observations, which for m > 2n, is generically an embedding. This is Takens' result. Our analytical examples show that it is possible to obtain spurious Lyapunov exponents that are even larger than the largest Lyapunov exponent of the original system. Therefore, we present examples where the largest Lyapunov exponent may not be preserved under Takens' embedding theorem. (C) 2000 Elsevier Science B.V.