Is the largest Lyapunov exponent preserved in embedded dynamics?

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