xt+1 = 1.0 + yt - A xt2
yt+1 = B xt
parameters: A = 1.4, B = 0.3
Lyapunov exponents (log with base-e): 0.4204, -1.6244
Lyapunov Dimension: 1.2588
The sum of the Lyapunov exponents is theoretically the same as ln(B).
Reference
A two-dimensional mapping with a strange attractor
Michel Hénon
Communications in Mathematical Physics, volume 50, 69–77 (1976)
DOI: 10.1007/BF01608556
Computing the Lyapunov spectrum of a dynamical system from an observed time series
Reggie Brown, Paul Bryant, and Henry Don Isaac Abarbanel
Physical Review A 43, 2787-2806 (1991)
Lyapunov Exponents without Rescaling and Reorthogonalization
Govindan Rangarajan, Salman Habib, and Robert D. Ryne
Physical Review Letters 80, 3747-3750 (1998)
programme
henon_lyap.c contains the main function.